{"id":27146,"date":"2021-03-28T13:00:14","date_gmt":"2021-03-28T13:00:14","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27146"},"modified":"2024-06-15T08:59:39","modified_gmt":"2024-06-15T08:59:39","slug":"%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/","title":{"rendered":"\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px; text-align:center;\">\n<h1>\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924<\/h1>\n<p>    <em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><br \/>\n        \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924, \u0907\u0938\u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e, \u0917\u0941\u0923 \u0914\u0930 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917\u094b\u0902 \u0915\u093e \u0905\u0928\u094d\u0935\u0947\u0937\u0923 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u092c\u0939\u0941\u092a\u0926 \u0917\u0923\u093f\u0924 \u0915\u093e \u090f\u0915 \u092e\u094c\u0932\u093f\u0915 \u0939\u093f\u0938\u094d\u0938\u093e \u0939\u0948\u0902 \u0914\u0930 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0935\u093f\u0937\u092f\u094b\u0902 \u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u092a\u0915 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u0930\u0916\u0924\u0947 \u0939\u0948\u0902\u0964<br \/>\n    <\/em><\/p>\n<p>    <strong>\u0938\u0940\u0916\u0928\u0947 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/strong><\/p>\n<p>\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u092e\u0947\u0902, \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947:<\/p>\n<p style=\"text-align:left;\">\n        1. \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0914\u0930 \u0909\u0928\u0915\u0947 \u0917\u0941\u0923\u094b\u0902 \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0914\u0930 \u0938\u092e\u091d\u0928\u093e\u0964<br \/>\n        2. \u092c\u0939\u0941\u092a\u0926 \u0915\u0940 \u0921\u093f\u0917\u094d\u0930\u0940 \u0914\u0930 \u0917\u0941\u0923\u093e\u0902\u0915 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0930\u0928\u093e\u0964<br \/>\n        3. \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901 \u0915\u0930\u0928\u093e \u0914\u0930 \u0917\u0923\u093f\u0924\u0940\u092f \u0938\u0902\u0926\u0930\u094d\u092d\u094b\u0902 \u092e\u0947\u0902 \u0909\u0928\u0915\u0947 \u0917\u0941\u0923\u094b\u0902 \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u093e\u0964\n    <\/p>\n<p>    <strong>\u0935\u093f\u0937\u092f-\u0938\u0942\u091a\u0940:<\/strong><\/p>\n<p>\n        <a href=\"#1\"><strong>1. \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901<\/strong><\/a><br \/>\n        <a href=\"#2\"><strong>2. \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0915\u093e\u0930<\/strong><\/a><br \/>\n        <a href=\"#3\"><strong>3. \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924: \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901<\/strong><\/a><br \/>\n        <a href=\"#4\"><strong>4. \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928<\/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. \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901<\/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;\">\u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092a\u0939\u0932\u0947 \u0939\u092e\u0947\u0902 \u091c\u093e\u0928\u0928\u093e \u0939\u094b\u0917\u093e \u0915\u093f \u092c\u0939\u0941\u092a\u0926 \u0915\u094d\u092f\u093e \u0939\u0948\u0902\u0964<\/span><\/strong><\/a> \u092c\u0939\u0941\u092a\u0926 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u092b\u0932\u0928 \u0939\u0948\u0902\u0964 \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u090f\u0915 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u091a\u0930 \u0939\u0948, \u0924\u094b \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u092b\u0932\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u090f\u0915 \u092c\u0939\u0941\u092a\u0926 \u0939\u0948 \u092f\u0926\u093f \u0907\u0938\u0947 \u0907\u0938 \u0930\u0942\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:\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    \u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0915\u094b\u0908 \u0917\u0948\u0930-\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0939\u0948 \u0914\u0930 \u0938\u092d\u0940 <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> \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0917\u0941\u0923\u093e\u0902\u0915 \u0939\u0948\u0902\u0964 \u092f\u0926\u093f \u0915\u094b\u0908 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0939\u0948 \u091c\u093f\u0938\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">a_k\\neq 0<\/span> \u0939\u0948 \u0914\u0930 \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">k\\lt i<\/span> \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b <span class=\"katex-eq\" data-katex-display=\"false\">a_i=0<\/span>, \u0924\u094b \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0907\u0938 \u092e\u093e\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0915\u094b <strong>\u092c\u0939\u0941\u092a\u0926 \u0915\u0940 \u0921\u093f\u0917\u094d\u0930\u0940<\/strong> \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u0926\u0942\u0938\u0930\u0947 \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902, \u092c\u0939\u0941\u092a\u0926 \u0915\u0940 \u0921\u093f\u0917\u094d\u0930\u0940 \u0935\u0939 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0940 \u0936\u0915\u094d\u0924\u093f \u0939\u0948 \u091c\u094b \u0915\u093f\u0938\u0940 \u0917\u0948\u0930-\u0936\u0942\u0928\u094d\u092f \u0917\u0941\u0923\u093e\u0902\u0915 \u0915\u0947 \u0938\u093e\u0925 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964\n<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2><strong>2. \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0915\u093e\u0930<\/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;\">\u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u094b \u0909\u0928\u0915\u0940 \u0921\u093f\u0917\u094d\u0930\u0940 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0935\u0930\u094d\u0917\u0940\u0915\u0943\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948;<\/span><\/strong><\/a> \u0907\u0938\u0940\u0932\u093f\u090f, \u091c\u092c \u0915\u093f\u0938\u0940 \u092c\u0939\u0941\u092a\u0926 \u0915\u093e \u0909\u0932\u094d\u0932\u0947\u0916 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0924\u094b \u0906\u092e\u0924\u094c\u0930 \u092a\u0930 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u092f\u0939 \u0921\u093f\u0917\u094d\u0930\u0940 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0915\u093e \u092c\u0939\u0941\u092a\u0926 \u0939\u0948, \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0935\u0939 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0940 \u0936\u0915\u094d\u0924\u093f \u0939\u094b\u0924\u0940 \u0939\u0948 \u091c\u094b \u0907\u0938 \u092c\u0939\u0941\u092a\u0926 \u0915\u0947 \u0917\u0948\u0930-\u0936\u0942\u0928\u094d\u092f \u0917\u0941\u0923\u093e\u0902\u0915 \u0915\u0947 \u0938\u093e\u0925 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964\n<\/p>\n<h3>2.1. \u0938\u094d\u0925\u093f\u0930 \u092c\u0939\u0941\u092a\u0926<\/h3>\n<p style=\"text-align: justify; color: #000000;\">\u092f\u0939 \u092a\u0930\u093f\u0935\u093e\u0930 \u0938\u092d\u0940 \u0936\u0942\u0928\u094d\u092f \u0921\u093f\u0917\u094d\u0930\u0940 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0914\u0930 \u0936\u0942\u0928\u094d\u092f \u092c\u0939\u0941\u092a\u0926 \u0915\u094b \u0938\u092e\u094d\u092e\u093f\u0932\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0939\u092e \u0915\u0939\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0915\u094b\u0908 \u092c\u0939\u0941\u092a\u0926 \u0936\u0942\u0928\u094d\u092f \u0921\u093f\u0917\u094d\u0930\u0940 \u0915\u093e \u0939\u0948, \u092f\u0926\u093f \u0907\u0938\u0947 \u0907\u0938 \u0930\u0942\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 <span class=\"katex-eq\" data-katex-display=\"false\">P(x)=c,<\/span> \u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">c\\neq 0.<\/span> \u0926\u0942\u0938\u0930\u0940 \u0913\u0930, \u0936\u0942\u0928\u094d\u092f \u092c\u0939\u0941\u092a\u0926 \u0907\u0938 \u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u094b\u0924\u093e \u0939\u0948 <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 0<\/span> \u0914\u0930 \u0907\u0938\u0915\u0947 \u0932\u093f\u090f \u0915\u094b\u0908 \u0921\u093f\u0917\u094d\u0930\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2><strong>3. \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924: \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901<\/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;\">\u092c\u0939\u0941\u092a\u0926 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0938\u0947 \u0905\u092a\u0928\u0940 \u0938\u092d\u0940 \u0917\u0941\u0923\u094b\u0902 \u0915\u094b \u0935\u093f\u0930\u093e\u0938\u0924 \u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/strong><\/a> \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0917\u0941\u0923 \u0935\u093f\u0924\u0930\u0923\u0940\u092f \u0914\u0930 \u0938\u0902\u0918\u0940\u092f \u0917\u0941\u0923 \u0939\u0948\u0902\u0964\n<\/p>\n<h3>3.1. \u091c\u094b\u0921\u093c \u0914\u0930 \u0918\u091f\u093e\u0935<\/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;\">\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">Q<\/span> \u0926\u094b \u092c\u0939\u0941\u092a\u0926 \u0939\u0948\u0902 \u091c\u093f\u0928\u0915\u0940 \u0921\u093f\u0917\u094d\u0930\u0940<\/span><\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0939\u0948, \u0915\u094d\u0930\u092e\u0936\u0903, \u091c\u093f\u0928\u092e\u0947\u0902<\/p>\n<p style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">m=n+k<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">0\\leq k,<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u0924\u094b \u092f\u0939 \u0939\u094b\u0917\u093e:<\/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;\">\u0905\u0930\u094d\u0925\u093e\u0924, <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0915\u0940 \u0938\u092e\u093e\u0928 \u0936\u0915\u094d\u0924\u093f\u092f\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0906\u0928\u0947 \u0935\u093e\u0932\u0947 \u0917\u0941\u0923\u093e\u0902\u0915 \u091c\u094b\u0921\u093c \u092f\u093e \u0918\u091f\u093e\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902, \u091c\u0948\u0938\u093e \u092d\u0940 \u0939\u094b\u0964<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000080;\">\u0909\u0926\u093e\u0939\u0930\u0923:<\/span><br \/>\n\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 3+5x+2x^2<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = 6x-3x^2 +23x^5<\/span>, \u0924\u094b:<\/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. \u0917\u0941\u0923\u0928<\/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;\">\u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u091c\u094b\u0921\u093c \u0914\u0930 \u0918\u091f\u093e\u0935 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902,<\/span><\/strong><\/a> \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u0917\u0941\u0923\u0928 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u093f\u0915\u0938\u093f\u0924 \u0939\u094b\u0917\u093e:\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    \u092a\u0939\u0932\u0947 \u0939\u092e \u0938\u094d\u0915\u0947\u0932\u0930 \u0917\u0941\u0923\u0928 \u0915\u094b \u0905\u0932\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">c \\in \\mathbb{R},<\/span> \u0924\u094b \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0939\u0948:\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    \u0914\u0930 \u092b\u093f\u0930 \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0917\u0941\u0923\u0928 \u0939\u094b\u0924\u093e \u0939\u0948:\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    \u092f\u0939 \u0935\u0939\u0940 \u0939\u0948 \u091c\u093f\u0938\u0947 \u0939\u092e \u00ab\u0938\u092c\u0915\u093e \u0938\u092c\u0915\u0947 \u0938\u093e\u0925 \u0917\u0941\u0923\u0928 \u0915\u093e \u092f\u094b\u0917\u00bb \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0938\u093e\u0930\u093e\u0902\u0936\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947\u0964\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span style=\"color: #000080;\">\u0909\u0926\u093e\u0939\u0930\u0923:<\/span><br \/>\n    \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">P(x) = 4x+ 2x^2-x^4<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x) = 5 - x + x^2-7x^3,<\/span> \u0924\u094b:\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. \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928<\/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;\">\u091c\u092c \u0939\u092e \u0926\u094b \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u094b \u0917\u0941\u0923\u093e \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e \u0926\u094b \u0938\u0930\u0932 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0938\u0947 \u0905\u0927\u093f\u0915 \u091c\u091f\u093f\u0932 \u092c\u0939\u0941\u092a\u0926 (\u0909\u091a\u094d\u091a \u0921\u093f\u0917\u094d\u0930\u0940 \u0935\u093e\u0932\u093e) \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/strong><\/a> \u091c\u092c \u0939\u092e \u0915\u093f\u0938\u0940 \u092c\u0939\u0941\u092a\u0926 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e \u0935\u093f\u092a\u0930\u0940\u0924 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u093e \u0905\u0928\u0941\u0938\u0930\u0923 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902: \u0939\u092e \u090f\u0915 \u091c\u091f\u093f\u0932 \u092c\u0939\u0941\u092a\u0926 \u0915\u094b \u0926\u094b \u092f\u093e \u0905\u0927\u093f\u0915 \u0928\u093f\u092e\u094d\u0928 \u0921\u093f\u0917\u094d\u0930\u0940 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u0917\u0941\u0923\u0928\u092b\u0932 \u092e\u0947\u0902 \u092c\u0926\u0932\u0924\u0947 \u0939\u0948\u0902\u0964\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    \u0915\u093f\u0938\u0940 \u092c\u0939\u0941\u092a\u0926 <span class=\"katex-eq\" data-katex-display=\"false\">P(x),<\/span> \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0939 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948 \u0915\u093f \u0909\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u094b \u0916\u094b\u091c\u093e \u091c\u093e\u090f \u091c\u094b \u092c\u0939\u0941\u092a\u0926 \u0915\u094b \u0936\u0942\u0928\u094d\u092f \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902; \u092f\u0926\u093f \u0910\u0938\u0947 \u092e\u093e\u0928 \u092e\u094c\u091c\u0942\u0926 \u0939\u0948\u0902, \u0924\u094b \u092c\u0939\u0941\u092a\u0926 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923\u0940\u092f \u0939\u0948\u0964 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u0915\u0940 \u092c\u093e\u0924 \u0915\u0930\u0928\u093e \u0938\u0941\u0932\u092d \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u0909\u0928\u094d\u0939\u0947\u0902 \u0916\u094b\u091c\u0928\u093e \u090f\u0915 \u0905\u0932\u0917 \u0915\u0939\u093e\u0928\u0940 \u0939\u0948\u0964 \u091c\u092c \u0939\u092e \u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0914\u0930 (2n)\u0926\u094d\u0935\u093f\u0918\u093e\u0924 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0947\u0902\u0917\u0947, \u0924\u094b \u0939\u092e \u0907\u0938 \u0935\u093f\u0937\u092f \u0915\u094b \u0905\u0927\u093f\u0915 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0938\u0947 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947\u0964\n<\/p>\n<h3>4.1. \u0909\u0932\u094d\u0932\u0947\u0916\u0928\u0940\u092f \u0909\u0924\u094d\u092a\u093e\u0926<\/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;\">\u0939\u093e\u0932\u093e\u0902\u0915\u093f, \u0910\u0938\u0947 \u092e\u093e\u092e\u0932\u0947 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u091c\u0939\u093e\u0901 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948,<\/span><\/strong><br \/>\n    <\/a> \u091c\u0948\u0938\u0947 \u0909\u0932\u094d\u0932\u0947\u0916\u0928\u0940\u092f \u0909\u0924\u094d\u092a\u093e\u0926\u0964 \u0907\u0928 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0915\u0941\u091b \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948\u0902:\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. \u0935\u093f\u092d\u093e\u091c\u0928 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u094d\u092e<\/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;\">\u091c\u0948\u0938\u0947 \u0915\u093f \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u093e \u0917\u0941\u0923\u0928 \u0915\u0930\u0928\u0947 \u0938\u0947 \u092f\u094c\u0917\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u094d\u092e \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0930\u0928\u0947 \u0938\u0947 \u091c\u092c \u0936\u0947\u0937\u092b\u0932 \u0936\u0942\u0928\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948,<\/span><\/strong><\/a> \u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0935\u093f\u092d\u093e\u091c\u0928 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u094d\u092e \u0915\u094b \u00ab\u092a\u093e\u0920\u00bb \u092e\u0947\u0902 \u0938\u092e\u091d\u093e\u0928\u093e \u0925\u094b\u0921\u093c\u093e \u091c\u091f\u093f\u0932 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948, \u0907\u0938\u0947 \u0938\u0940\u0927\u0947 \u0926\u0947\u0916\u0915\u0930 \u0938\u092e\u091d\u0928\u093e \u0914\u0930 \u0915\u093f\u0928 \u092e\u093e\u092e\u0932\u094b\u0902 \u092e\u0947\u0902 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0925\u094d\u092e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0940 \u0913\u0930 \u0932\u0947 \u091c\u093e\u0924\u093e \u0939\u0948, \u092f\u0939 \u092c\u0939\u0941\u0924 \u0906\u0938\u093e\u0928 \u0939\u0948\u0964 \u0907\u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e \u0915\u0941\u091b \u0909\u0926\u093e\u0939\u0930\u0923\u094b\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947\u0964\n<\/p>\n<p style=\"text-align: justify; color: #000000;\">\n    <span style=\"color: #000080;\">\u0909\u0926\u093e\u0939\u0930\u0923:<\/span> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092e\u093e\u092e\u0932\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f <span class=\"katex-eq\" data-katex-display=\"false\">P(x):Q(x)<\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902:\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;\">[\u0938\u092e\u093e\u0927\u093e\u0928]<\/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>[\u0938\u092e\u093e\u0927\u093e\u0928]<\/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>[\u0938\u092e\u093e\u0927\u093e\u0928]<\/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>[\u0938\u092e\u093e\u0927\u093e\u0928]<\/strong><\/span> <\/a>\n    <\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0938\u093e\u0930\u093e\u0902\u0936: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924, \u0907\u0938\u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e, \u0917\u0941\u0923 \u0914\u0930 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917\u094b\u0902 \u0915\u093e \u0905\u0928\u094d\u0935\u0947\u0937\u0923 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u092c\u0939\u0941\u092a\u0926 \u0917\u0923\u093f\u0924 \u0915\u093e \u090f\u0915 \u092e\u094c\u0932\u093f\u0915 \u0939\u093f\u0938\u094d\u0938\u093e \u0939\u0948\u0902 \u0914\u0930 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0935\u093f\u0937\u092f\u094b\u0902 \u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u092a\u0915 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u0930\u0916\u0924\u0947 \u0939\u0948\u0902\u0964 \u0938\u0940\u0916\u0928\u0947 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u092e\u0947\u0902, \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947: 1. \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0914\u0930 \u0909\u0928\u0915\u0947 \u0917\u0941\u0923\u094b\u0902 \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 [&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":1,"footnotes":""},"categories":[577,593],"tags":[],"class_list":["post-27146","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-577","category-593"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u091c\u093e\u0928\u0947\u0902: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901, \u092a\u094d\u0930\u0915\u093e\u0930, \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901, \u0917\u0941\u0923\u0928\u092b\u0932, \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928\u0964\" \/>\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\/hi\/\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915-\u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902-\u0915\u0947-\u092c\u0939\u0941\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924\" \/>\n<meta property=\"og:description\" content=\"\u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u091c\u093e\u0928\u0947\u0902: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901, \u092a\u094d\u0930\u0915\u093e\u0930, \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901, \u0917\u0941\u0923\u0928\u092b\u0932, \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928\u0964\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/hi\/\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915-\u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902-\u0915\u0947-\u092c\u0939\u0941\/\" \/>\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=\"2021-03-28T13:00:14+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-06-15T08:59:39+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=\"\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924\" \/>\n<meta name=\"twitter:description\" content=\"\u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u091c\u093e\u0928\u0947\u0902: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901, \u092a\u094d\u0930\u0915\u093e\u0930, \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901, \u0917\u0941\u0923\u0928\u092b\u0932, \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928\u0964\" \/>\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\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924\",\"datePublished\":\"2021-03-28T13:00:14+00:00\",\"dateModified\":\"2024-06-15T08:59:39+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/\"},\"wordCount\":545,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg\",\"articleSection\":[\"\u0917\u0923\u093f\u0924\",\"\u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0914\u0930 \u0930\u0947\u0916\u093e\u0917\u0923\u093f\u0924\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/\",\"url\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/\",\"name\":\"\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924 - toposuranos.com\/material\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#primaryimage\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg\",\"datePublished\":\"2021-03-28T13:00:14+00:00\",\"dateModified\":\"2024-06-15T08:59:39+00:00\",\"description\":\"\u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u091c\u093e\u0928\u0947\u0902: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901, \u092a\u094d\u0930\u0915\u093e\u0930, \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901, \u0917\u0941\u0923\u0928\u092b\u0932, \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928\u0964\",\"breadcrumb\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#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\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924\"}]},{\"@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":"\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924 - toposuranos.com\/material","description":"\u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u091c\u093e\u0928\u0947\u0902: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901, \u092a\u094d\u0930\u0915\u093e\u0930, \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901, \u0917\u0941\u0923\u0928\u092b\u0932, \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928\u0964","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\/hi\/\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915-\u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902-\u0915\u0947-\u092c\u0939\u0941\/","og_locale":"es_ES","og_type":"article","og_title":"\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924","og_description":"\u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u091c\u093e\u0928\u0947\u0902: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901, \u092a\u094d\u0930\u0915\u093e\u0930, \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901, \u0917\u0941\u0923\u0928\u092b\u0932, \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928\u0964","og_url":"http:\/\/toposuranos.com\/material\/hi\/\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915-\u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902-\u0915\u0947-\u092c\u0939\u0941\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-03-28T13:00:14+00:00","article_modified_time":"2024-06-15T08:59:39+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":"\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924","twitter_description":"\u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u091c\u093e\u0928\u0947\u0902: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901, \u092a\u094d\u0930\u0915\u093e\u0930, \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901, \u0917\u0941\u0923\u0928\u092b\u0932, \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928\u0964","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\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924","datePublished":"2021-03-28T13:00:14+00:00","dateModified":"2024-06-15T08:59:39+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/"},"wordCount":545,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg","articleSection":["\u0917\u0923\u093f\u0924","\u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0914\u0930 \u0930\u0947\u0916\u093e\u0917\u0923\u093f\u0924"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/","url":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/","name":"\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924 - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/03\/polinomios.jpg","datePublished":"2021-03-28T13:00:14+00:00","dateModified":"2024-06-15T08:59:39+00:00","description":"\u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u091c\u093e\u0928\u0947\u0902: \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901, \u092a\u094d\u0930\u0915\u093e\u0930, \u0938\u0902\u0915\u094d\u0930\u093f\u092f\u093e\u090f\u0901, \u0917\u0941\u0923\u0928\u092b\u0932, \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928\u0964","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#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\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%b8%e0%a5%8d%e0%a4%a4%e0%a4%b5%e0%a4%bf%e0%a4%95-%e0%a4%b8%e0%a4%82%e0%a4%96%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%93%e0%a4%82-%e0%a4%95%e0%a5%87-%e0%a4%ac%e0%a4%b9%e0%a5%81\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924"}]},{"@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\/27146","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=27146"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/27146\/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=27146"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=27146"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=27146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}