{"id":27149,"date":"2021-03-28T13:00:37","date_gmt":"2021-03-28T13:00:37","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27149"},"modified":"2024-06-15T09:05:16","modified_gmt":"2024-06-15T09:05:16","slug":"%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/","title":{"rendered":"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px; text-align:center;\">\n<h1>\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b<\/h1>\n<p>    <em><strong>\u0420\u0435\u0437\u044e\u043c\u0435:<\/strong><br \/>\n        \u0412 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0430\u043b\u0433\u0435\u0431\u0440\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432, \u0438\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435, \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f. \u041c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0432\u0430\u0436\u043d\u043e\u0439 \u0447\u0430\u0441\u0442\u044c\u044e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0438 \u0438\u043c\u0435\u044e\u0442 \u0448\u0438\u0440\u043e\u043a\u043e\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u0432 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0434\u0438\u0441\u0446\u0438\u043f\u043b\u0438\u043d\u0430\u0445.<br \/>\n    <\/em><\/p>\n<p>    <strong>\u0426\u0415\u041b\u0418 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u042f<\/strong><\/p>\n<p>\u041f\u043e\u0441\u043b\u0435 \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u043e\u043a\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u044b \u0441\u043c\u043e\u0433\u0443\u0442:<\/p>\n<p style=\"text-align:left;\">\n        1. \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442\u044c \u0438 \u043f\u043e\u043d\u0438\u043c\u0430\u0442\u044c \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u0438 \u0438\u0445 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430.<br \/>\n        2. \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430.<br \/>\n        3. \u0412\u044b\u043f\u043e\u043b\u043d\u044f\u0442\u044c \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u0441 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430\u043c\u0438 \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c \u0438\u0445 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u043a\u043e\u043d\u0442\u0435\u043a\u0441\u0442\u0435.\n    <\/p>\n<p>    <strong>\u0421\u041e\u0414\u0415\u0420\u0416\u0410\u041d\u0418\u0415:<\/strong><\/p>\n<p>\n        <a href=\"#1\"><strong>1. \u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432: \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f<\/strong><\/a><br \/>\n        <a href=\"#2\"><strong>2. \u0422\u0438\u043f\u044b \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432<\/strong><\/a><br \/>\n        <a href=\"#3\"><strong>3. \u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432: \u041e\u043f\u0435\u0440\u0430\u0446\u0438\u0438<\/strong><\/a><br \/>\n        <a href=\"#4\"><strong>4. \u0424\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432<\/strong><\/a>\n    <\/p>\n<p>    <iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ry4sKaS3RMc\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<\/div>\n<p><a name=\"1\"><\/a><\/p>\n<h2><strong>1. \u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432: \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f<\/strong><\/h2>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=139s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong><span style=\"color: #ff0000;\">\u0427\u0442\u043e\u0431\u044b \u043f\u043e\u043d\u044f\u0442\u044c \u0430\u043b\u0433\u0435\u0431\u0440\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432, \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u043d\u0443\u0436\u043d\u043e \u0443\u0437\u043d\u0430\u0442\u044c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b.<\/span><\/strong><\/a> \u041c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u2014 \u044d\u0442\u043e \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u2014 \u044d\u0442\u043e \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u0430\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f, \u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u043c, \u0435\u0441\u043b\u0438 \u043e\u043d\u0430 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0437\u0430\u043f\u0438\u0441\u0430\u043d\u0430 \u0432 \u0432\u0438\u0434\u0435:\n<\/p>\n<p style=\"text-align: center; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P(x)= \\sum_{i=0}^n a_i x^i= a_0 + a_1x + a_2x^2 + a_3x^3 + \\cdots + a_nx^n,<\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    \u0433\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u2014 \u044d\u0442\u043e \u043d\u0435\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0446\u0435\u043b\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u0430 \u0432\u0441\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">a_i<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">i\\in\\{1,2,3,\\cdots,n\\},<\/span> \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0430\u043c\u0438. \u0415\u0441\u043b\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span>, \u0442\u0430\u043a\u043e\u0435 \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">a_k\\neq 0<\/span> \u0438, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">k\\lt i<\/span>, \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f <span class=\"katex-eq\" data-katex-display=\"false\">a_i=0<\/span>, \u0442\u043e \u0433\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\u0442\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u0441\u0442\u0435\u043f\u0435\u043d\u044c\u044e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430.<\/strong> \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430 \u2014 \u044d\u0442\u043e \u043d\u0430\u0438\u0431\u043e\u043b\u044c\u0448\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u044c, \u0441\u043e\u043f\u0440\u043e\u0432\u043e\u0436\u0434\u0430\u044e\u0449\u0430\u044f\u0441\u044f \u043d\u0435\u043d\u0443\u043b\u0435\u0432\u044b\u043c \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u043c.\n<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2><strong>2. \u0422\u0438\u043f\u044b \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432<\/strong><\/h2>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=340s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong><span style=\"color: #ff0000;\">\u041c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u043a\u043b\u0430\u0441\u0441\u0438\u0444\u0438\u0446\u0438\u0440\u0443\u044e\u0442\u0441\u044f \u043f\u043e \u0438\u0445 \u0441\u0442\u0435\u043f\u0435\u043d\u0438;<\/span><\/strong><\/a> \u043f\u043e\u044d\u0442\u043e\u043c\u0443, \u043a\u043e\u0433\u0434\u0430 \u0443\u043f\u043e\u043c\u0438\u043d\u0430\u0435\u0442\u0441\u044f \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d, \u043e\u0431\u044b\u0447\u043d\u043e \u0433\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\u0442\u043e \u044d\u0442\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u0441\u0442\u0435\u043f\u0435\u043d\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span>, \u043a\u043e\u0433\u0434\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u2014 \u044d\u0442\u043e \u043d\u0430\u0438\u0431\u043e\u043b\u044c\u0448\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u044c <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>, \u0441\u043e\u043f\u0440\u043e\u0432\u043e\u0436\u0434\u0430\u044e\u0449\u0430\u044f \u043d\u0435\u043d\u0443\u043b\u0435\u0432\u043e\u0439 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u044d\u0442\u043e\u0433\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430.\n<\/p>\n<h3>2.1. \u041f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u044b\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u042d\u0442\u043e \u0441\u0435\u043c\u0435\u0439\u0441\u0442\u0432\u043e \u0432\u043a\u043b\u044e\u0447\u0430\u0435\u0442 \u0432 \u0441\u0435\u0431\u044f \u0432\u0441\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u043d\u0443\u043b\u0435\u0432\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0438 \u043d\u0443\u043b\u0435\u0432\u043e\u0439 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d. \u041c\u044b \u0433\u043e\u0432\u043e\u0440\u0438\u043c, \u0447\u0442\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u0438\u043c\u0435\u0435\u0442 \u043d\u0443\u043b\u0435\u0432\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c, \u0435\u0441\u043b\u0438 \u0435\u0433\u043e \u043c\u043e\u0436\u043d\u043e \u0437\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u0432 \u0432\u0438\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">P(x)=c,<\/span> \u0433\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">c\\neq 0.<\/span> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043d\u0443\u043b\u0435\u0432\u043e\u0439 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434 <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 0<\/span>, \u0438 \u0435\u0433\u043e \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u043d\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2><strong>3. \u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432: \u041e\u043f\u0435\u0440\u0430\u0446\u0438\u0438<\/strong><\/h2>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=428s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong><span style=\"color: #ff0000;\">\u041c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u043d\u0430\u0441\u043b\u0435\u0434\u0443\u044e\u0442 \u0432\u0441\u0435 \u0441\u0432\u043e\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0438\u0437 \u0430\u043b\u0433\u0435\u0431\u0440\u044b \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b.<\/span><\/strong><\/a> \u041e\u0441\u043e\u0431\u0435\u043d\u043d\u043e \u0432\u0430\u0436\u043d\u044b \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0438 \u0430\u0441\u0441\u043e\u0446\u0438\u0430\u0442\u0438\u0432\u043d\u044b\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430.\n<\/p>\n<h3>3.1. \u0421\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=470s\" target=\"_blank\" rel=\"noopener\"> <strong><span style=\"color: #ff0000;\">\u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">Q<\/span> \u2014 \u044d\u0442\u043e \u0434\u0432\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0438<\/span><\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u043f\u0440\u0438<\/p>\n<p style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">m=n+k<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">0\\leq k,<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u0442\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\displaystyle P(x) \\pm Q(x) &amp;=\\displaystyle \\sum_{i=0}^n a_i x^i \\pm \\sum_{i=0}^m b_i x^i \\\\ \\\\\n\n &amp;\\displaystyle = \\sum_{i=0}^n a_i x^i \\pm \\left( \\sum_{i=0}^n b_i x^i + \\sum_{i=n+1}^{n+k} b_i x^i \\right) \\\\ \\\\\n\n&amp;\\displaystyle = \\sum_{i=0}^n (a_i \\pm b_i) x^i + \\sum_{i=n+1}^m b_i x^i\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u0422\u043e \u0435\u0441\u0442\u044c \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043f\u0440\u0438 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u0445 \u0441\u0442\u0435\u043f\u0435\u043d\u044f\u0445 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0441\u043a\u043b\u0430\u0434\u044b\u0432\u0430\u044e\u0442\u0441\u044f \u0438\u043b\u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u044e\u0442\u0441\u044f, \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u0442 \u0441\u043b\u0443\u0447\u0430\u044f.<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000080;\">\u041f\u0420\u0418\u041c\u0415\u0420:<\/span><br \/>\n\u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 3+5x+2x^2<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = 6x-3x^2 +23x^5<\/span>, \u0442\u043e:<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">P(x) + Q(x) = \\cdots \\\\ = (3+5x+2x^2) + (6x-3x^2 +23x^5) \\\\ = 3 + (5+6)x + (2-3)x^2 + 23x^5 \\\\ = 3 + 11x - x^2 + 23x^5 <\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">P(x) - Q(x) = \\cdots \\\\ = (3+5x+2x^2) - (6x-3x^2 +23x^5) \\\\ = 3 + (5-6)x + (2+3)x^2 - 23x^5 \\\\ = 3 - x + 5x^2 - 23x^5 <\/span>\n<\/p>\n<h3>3.2. \u0423\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=894s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0412 \u0442\u043e\u043c \u0436\u0435 \u043a\u043e\u043d\u0442\u0435\u043a\u0441\u0442\u0435, \u0447\u0442\u043e \u0438 \u0434\u043b\u044f \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u044f \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432,<\/span><\/strong><\/a> \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0437\u0432\u0438\u0432\u0430\u0442\u044c\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0440\u0430\u0437\u043b\u0438\u0447\u0430\u0435\u043c \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 \u0441\u043a\u0430\u043b\u044f\u0440. \u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">c \\in \\mathbb{R},<\/span> \u0442\u043e \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c:\n<\/p>\n<p style=\"text-align: center; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle c P(x) = c \\sum_{i=0}^n a_i x^i =\\sum_{i=0}^n c a_i x^i <\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    \u0410 \u0437\u0430\u0442\u0435\u043c \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430\u043c\u0438:\n<\/p>\n<p style=\"text-align: center; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\displaystyle P(x) Q(x) &amp;\\displaystyle = \\left( \\sum_{i=0}^n a_i x^i \\right) \\left(\\sum_{j=0}^m b_j x^j\\right) \\\\ \\\\\n\n&amp;=\\displaystyle \\left[\\sum_{j=0}^m \\left( \\sum_{i=0}^n a_i x^i \\right) b_j x^j\\right] \\\\ \\\\\n\n&amp;=\\displaystyle \\ sum_{j=0}^m \\left( \\ sum_{i=0}^n a_ib_j x^{i+j} \\ right) \\\\ \\\\\n\n&amp;=\\displaystyle \\ sum_{i,j=0}^{n,m} a_ib_j x^{i+j}\n\n\\end{array}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\n    \u042d\u0442\u043e \u0442\u043e, \u0447\u0442\u043e \u043c\u044b \u0431\u044b \u0441\u0443\u043c\u043c\u0438\u0440\u043e\u0432\u0430\u043b\u0438 \u0447\u0435\u0440\u0435\u0437 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u00ab\u0441\u0443\u043c\u043c\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0439 \u0432\u0441\u0435\u0445 \u043d\u0430 \u0432\u0441\u0435\u0445\u00bb.\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span style=\"color: #000080;\">\u041f\u0420\u0418\u041c\u0415\u0420:<\/span><br \/>\n    \u0415\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 4x+ 2x^2-x^4<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = 5 - x + x^2-7x^3,<\/span> \u0442\u043e:\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">P(x)Q(x) =\\cdots \\\\ {} \\\\= (4x+ 2x^2-x^4)(5 - x + x^2-7x^3) \\\\ {} \\\\ = 4x(5 - x + x^2-7x^3) \\\\ + 2x^2 (5 - x + x^2-7x^3) \\\\ - x^4 (5 - x + x^2-7x^3) \\\\ {} \\\\ = 20x - 4x^2 + 4x^3 - 28x^4 \\\\ + 10x^2 - 2x^3 + 2x^4 - 14x^5 \\\\ -5x^4 + x^5 - x^6 + 7x^7 \\\\ {} \\\\ = 20x + 6x^2 + 2x^3 - 31x^4 - 13x^5 - x^6 + 7x^7<\/span>\n<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2><strong>4. \u0424\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432<\/strong><\/h2>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=1375s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong><span style=\"color: #ff0000;\">\u041a\u043e\u0433\u0434\u0430 \u043c\u044b \u0443\u043c\u043d\u043e\u0436\u0430\u0435\u043c \u0434\u0432\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430, \u043c\u044b \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u043c \u043e\u0442 \u0434\u0432\u0443\u0445 \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u043a \u0431\u043e\u043b\u0435\u0435 \u0441\u043b\u043e\u0436\u043d\u043e\u043c\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0443 (\u0432\u044b\u0441\u0448\u0435\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438).<\/span><\/strong><\/a> \u041a\u043e\u0433\u0434\u0430 \u043c\u044b \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0443\u0435\u043c \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d, \u043c\u044b \u0441\u043b\u0435\u0434\u0443\u0435\u043c \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u043c\u0443 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0443: \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0441\u043b\u043e\u0436\u043d\u044b\u0439 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u0432 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0438\u043b\u0438 \u0431\u043e\u043b\u0435\u0435 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u043d\u0438\u0437\u0448\u0435\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438.\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    \u0427\u0442\u043e\u0431\u044b \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d <span class=\"katex-eq\" data-katex-display=\"false\">P(x),<\/span> \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043d\u0430\u0439\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span>, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0434\u0435\u043b\u0430\u044e\u0442 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u0440\u0430\u0432\u043d\u044b\u043c \u043d\u0443\u043b\u044e; \u0435\u0441\u043b\u0438 \u0442\u0430\u043a\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442, \u0442\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0443\u0435\u043c. \u0413\u043e\u0432\u043e\u0440\u0438\u0442\u044c \u043e\u0431 \u0438\u0445 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043e\u0432\u0430\u043d\u0438\u0438 \u043b\u0435\u0433\u043a\u043e, \u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u0438\u0445 \u2014 \u044d\u0442\u043e \u0434\u0440\u0443\u0433\u0430\u044f \u0438\u0441\u0442\u043e\u0440\u0438\u044f. \u041c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u044d\u0442\u043e\u0442 \u0432\u043e\u043f\u0440\u043e\u0441 \u0431\u043e\u043b\u0435\u0435 \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e, \u043a\u043e\u0433\u0434\u0430 \u0431\u0443\u0434\u0435\u043c \u0438\u0437\u0443\u0447\u0430\u0442\u044c \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u0438 (2n)-\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432.\n<\/p>\n<h3>4.1. \u0418\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=1654s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong><span style=\"color: #ff0000;\">\u041e\u0434\u043d\u0430\u043a\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0441\u043b\u0443\u0447\u0430\u0438, \u043a\u043e\u0433\u0434\u0430 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0434\u043e\u0441\u0442\u0438\u0433\u0430\u0435\u0442\u0441\u044f \u043b\u0435\u0433\u043a\u043e,<\/span><\/strong><br \/>\n    <\/a> \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f. \u041d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0438\u0437 \u044d\u0442\u0438\u0445 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u0432 \u0442\u0430\u043a\u043e\u0432\u044b:\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">x^2 - y^2 = (x-y)(x+y)<\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">(x\\pm y)^2 = x^2 \\pm 2xy + y^2<\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">(x \\pm y)^3 = x^3 \\pm 3x^2y + 3xy^2 \\pm y^3<\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">x^3-y^3=(x-y)(x^2+xy+y^2)<\/span>\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span class=\"katex-eq\" data-katex-display=\"false\">x^3+y^3=(x+y)(x^2-xy+y^2)<\/span>\n<\/p>\n<h3>4. \u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0434\u0435\u043b\u0435\u043d\u0438\u044f<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\n    <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=1854s\" target=\"_blank\" rel=\"noopener\"><br \/>\n        <strong><span style=\"color: #ff0000;\">\u0422\u0430\u043a \u0436\u0435, \u043a\u0430\u043a \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u0446\u0435\u043b\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u0434\u0430\u0435\u0442 \u0441\u043e\u0441\u0442\u0430\u0432\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430, \u0430 \u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 \u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u043e\u0432\u0430\u0442\u044c, \u043a\u043e\u0433\u0434\u0430 \u043e\u0441\u0442\u0430\u0442\u043e\u043a \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e,<\/span><\/strong><\/a> \u043d\u0435\u0447\u0442\u043e \u043f\u043e\u0434\u043e\u0431\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u0441 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430\u043c\u0438. \u041e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u044c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0434\u0435\u043b\u0435\u043d\u0438\u044f \u00ab\u0442\u0435\u043a\u0441\u0442\u043e\u043c\u00bb \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u0441\u043b\u043e\u0436\u043d\u043e, \u0433\u043e\u0440\u0430\u0437\u0434\u043e \u043b\u0435\u0433\u0447\u0435 \u043f\u043e\u043d\u044f\u0442\u044c, \u043d\u0430\u0431\u043b\u044e\u0434\u0430\u044f \u043d\u0435\u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u043a\u0430\u043a \u044d\u0442\u043e \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f \u0438 \u0432 \u043a\u0430\u043a\u0438\u0445 \u0441\u043b\u0443\u0447\u0430\u044f\u0445 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043f\u0440\u0438\u0432\u043e\u0434\u0438\u0442 \u043a \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u0438. \u0414\u043b\u044f \u0434\u043e\u0441\u0442\u0438\u0436\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432.\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span style=\"color: #000080;\">\u041f\u0420\u0418\u041c\u0415\u0420:<\/span> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c <span class=\"katex-eq\" data-katex-display=\"false\">P(x):Q(x)<\/span> \u0434\u043b\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0441\u043b\u0443\u0447\u0430\u0435\u0432:\n<\/p>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\n        <span class=\"katex-eq\" data-katex-display=\"false\">P(x)=2 x^3 + x^2 - 2 x - 1, <\/span> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)=x-1<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=1930s\" target=\"_blank\" rel=\"noopener\"> <strong><span style=\"color: #ff0000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong> <\/a>\n    <\/li>\n<li>\n        <span class=\"katex-eq\" data-katex-display=\"false\">P(x)=x^4+2x^3-x+1, <\/span> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)=x^2-4<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=2120s\" target=\"_blank\" rel=\"noopener\"> <span style=\"color: #ff0000;\"><strong>[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/strong><\/span> <\/a>\n    <\/li>\n<li>\n        <span class=\"katex-eq\" data-katex-display=\"false\">P(x)=3 x^4 - 2 x^3 - x^2 - 4 x + 1, <\/span> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)=x^2+x+1<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=2331s\" target=\"_blank\" rel=\"noopener\"> <span style=\"color: #ff0000;\"><strong>[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/strong><\/span> <\/a>\n    <\/li>\n<li>\n        <span class=\"katex-eq\" data-katex-display=\"false\">P(x)=x^7+5x^4+5x^2-3x+1, <\/span> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)=x^3-2x^2+1<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=ry4sKaS3RMc&amp;t=2464s\" target=\"_blank\" rel=\"noopener\"> <span style=\"color: #ff0000;\"><strong>[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/strong><\/span> <\/a>\n    <\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u0420\u0435\u0437\u044e\u043c\u0435: \u0412 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0430\u043b\u0433\u0435\u0431\u0440\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432, \u0438\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435, \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f. \u041c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0432\u0430\u0436\u043d\u043e\u0439 \u0447\u0430\u0441\u0442\u044c\u044e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0438 \u0438\u043c\u0435\u044e\u0442 \u0448\u0438\u0440\u043e\u043a\u043e\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u0432 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0434\u0438\u0441\u0446\u0438\u043f\u043b\u0438\u043d\u0430\u0445. \u0426\u0415\u041b\u0418 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u042f \u041f\u043e\u0441\u043b\u0435 \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u043e\u043a\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u044b \u0441\u043c\u043e\u0433\u0443\u0442: 1. \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442\u044c \u0438 \u043f\u043e\u043d\u0438\u043c\u0430\u0442\u044c \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u044b \u0438 \u0438\u0445 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430. 2. \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430. 3. \u0412\u044b\u043f\u043e\u043b\u043d\u044f\u0442\u044c \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27134,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":2,"footnotes":""},"categories":[589,573],"tags":[],"class_list":["post-27149","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-589","category-573"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u0430\u043b\u0433\u0435\u0431\u0440\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432: \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0442\u0438\u043f\u044b, \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0434\u0435\u043b\u0435\u043d\u0438\u0435.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/ru\/\u0430\u043b\u0433\u0435\u0431\u0440\u0430-\u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432-\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b\" \/>\n<meta property=\"og:description\" content=\"\u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u0430\u043b\u0433\u0435\u0431\u0440\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432: \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0442\u0438\u043f\u044b, \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0434\u0435\u043b\u0435\u043d\u0438\u0435.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/ru\/\u0430\u043b\u0433\u0435\u0431\u0440\u0430-\u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432-\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-03-28T13:00:37+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-06-15T09:05:16+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b\" \/>\n<meta name=\"twitter:description\" content=\"\u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u0430\u043b\u0433\u0435\u0431\u0440\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432: \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0442\u0438\u043f\u044b, \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0434\u0435\u043b\u0435\u043d\u0438\u0435.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b\",\"datePublished\":\"2021-03-28T13:00:37+00:00\",\"dateModified\":\"2024-06-15T09:05:16+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/\"},\"wordCount\":1025,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg\",\"articleSection\":[\"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u0438 \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f\",\"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/\",\"url\":\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/\",\"name\":\"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b - toposuranos.com\/material\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#primaryimage\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg\",\"datePublished\":\"2021-03-28T13:00:37+00:00\",\"dateModified\":\"2024-06-15T09:05:16+00:00\",\"description\":\"\u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u0430\u043b\u0433\u0435\u0431\u0440\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432: \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0442\u0438\u043f\u044b, \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0434\u0435\u043b\u0435\u043d\u0438\u0435.\",\"breadcrumb\":{\"@id\":\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#primaryimage\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg\",\"width\":1024,\"height\":356,\"caption\":\"Created with GIMP\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\/\/toposuranos.com\/material\/#website\",\"url\":\"http:\/\/toposuranos.com\/material\/\",\"name\":\"toposuranos.com\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\/\/toposuranos.com\/material\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\",\"name\":\"toposuranos.com\/material\",\"url\":\"http:\/\/toposuranos.com\/material\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\/material\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/groups\/toposuranos\",\"https:\/\/x.com\/topuranos\",\"https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\/\/www.linkedin.com\/company\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\/\/toposuranos.com\/material\"],\"url\":\"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b - toposuranos.com\/material","description":"\u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u0430\u043b\u0433\u0435\u0431\u0440\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432: \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0442\u0438\u043f\u044b, \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0434\u0435\u043b\u0435\u043d\u0438\u0435.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"http:\/\/toposuranos.com\/material\/ru\/\u0430\u043b\u0433\u0435\u0431\u0440\u0430-\u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432-\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445\/","og_locale":"es_ES","og_type":"article","og_title":"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b","og_description":"\u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u0430\u043b\u0433\u0435\u0431\u0440\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432: \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0442\u0438\u043f\u044b, \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0434\u0435\u043b\u0435\u043d\u0438\u0435.","og_url":"http:\/\/toposuranos.com\/material\/ru\/\u0430\u043b\u0433\u0435\u0431\u0440\u0430-\u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432-\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-03-28T13:00:37+00:00","article_modified_time":"2024-06-15T09:05:16+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b","twitter_description":"\u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u0430\u043b\u0433\u0435\u0431\u0440\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432: \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0442\u0438\u043f\u044b, \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0434\u0435\u043b\u0435\u043d\u0438\u0435.","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"1 minuto"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b","datePublished":"2021-03-28T13:00:37+00:00","dateModified":"2024-06-15T09:05:16+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/"},"wordCount":1025,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg","articleSection":["\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u0438 \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f","\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/","url":"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/","name":"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg","datePublished":"2021-03-28T13:00:37+00:00","dateModified":"2024-06-15T09:05:16+00:00","description":"\u0418\u0437\u0443\u0447\u0438\u0442\u0435 \u0430\u043b\u0433\u0435\u0431\u0440\u0443 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432: \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0442\u0438\u043f\u044b, \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0434\u0435\u043b\u0435\u043d\u0438\u0435.","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg","width":1024,"height":356,"caption":"Created with GIMP"},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/ru\/%d0%b0%d0%bb%d0%b3%d0%b5%d0%b1%d1%80%d0%b0-%d0%bc%d0%bd%d0%be%d0%b3%d0%be%d1%87%d0%bb%d0%b5%d0%bd%d0%be%d0%b2-%d0%b4%d0%b5%d0%b9%d1%81%d1%82%d0%b2%d0%b8%d1%82%d0%b5%d0%bb%d1%8c%d0%bd%d1%8b%d1%85\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u043e\u0432 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b"}]},{"@type":"WebSite","@id":"http:\/\/toposuranos.com\/material\/#website","url":"http:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"http:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"http:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/27149","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=27149"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/27149\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/27134"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=27149"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=27149"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=27149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}