{"id":857,"date":"2024-05-01T08:09:29","date_gmt":"2024-05-01T08:09:29","guid":{"rendered":"https:\/\/gbelentzas.sites.sch.gr\/?p=857"},"modified":"2024-05-01T15:26:27","modified_gmt":"2024-05-01T15:26:27","slug":"%ce%b5%ce%ba%cf%86%cf%89%ce%bd%ce%ae%cf%83%ce%b5%ce%b9%cf%82-%ce%b1%cf%80%ce%bf%ce%b4%ce%b5%ce%af%ce%be%ce%b5%cf%89%ce%bd-%ce%b1-%ce%bb%cf%85%ce%ba%ce%b5%ce%af%ce%bf%cf%85","status":"publish","type":"post","link":"https:\/\/gbelentzas.sites.sch.gr\/?p=857","title":{"rendered":"\u0395\u03ba\u03c6\u03c9\u03bd\u03ae\u03c3\u03b5\u03b9\u03c2 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c9\u03bd (\u0391 \u039b\u03c5\u03ba\u03b5\u03af\u03bf\u03c5)"},"content":{"rendered":"

\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 1<\/strong>. N\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 <\/span><\/span>\"\textcolor{blue}{\alpha, \beta \in R}\" \u00a0\u03b9\u03c3\u03c7\u03cd\u03b5\u03b9<\/span> <\/p>\n

  <\/span>   <\/span>\"\[\textcolor{blue}{|\alpha \cdot \beta|=|\alpha| \cdot|\beta|}\]\"<\/p>\n

\u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce<\/strong><\/a><\/span> \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7.<\/em><\/span><\/p>\n

\n

\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 2<\/strong>. N\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9<\/span> \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5<\/span> \"\textcolor{blue}{\alpha\in R}\" \u00a0\u03ba\u03b1\u03b9<\/span> \u00a0\"\textcolor{blue}{\beta \in R^{*}}\" \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 <\/span><\/span><\/p>\n

  <\/span>   <\/span>\"\[\textcolor{blue}{\left|\dfrac{\alpha}{\beta}\right|=\dfrac{|\alpha|}{|\beta|}}\]\"<\/p>\n

\u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce<\/strong><\/a><\/span> \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7.<\/em><\/span><\/p>\n

\n

\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 3<\/strong>. N\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9<\/span> \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5<\/span> \"\textcolor{blue}{ \alpha, \beta \in R}\" \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9<\/span> <\/p>\n

  <\/span>   <\/span>\"\[\textcolor{blue}{|\alpha+\beta| \leq|\alpha|+|\beta| }\]\"<\/p>\n

<\/span><\/p>\n

\u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce<\/strong><\/a><\/span> \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7.<\/em><\/span><\/p>\n

\n

\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 4<\/strong>. N\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 <\/span><\/span> \"\textcolor{blue}{\alpha, \beta \in R }\"<\/span>\u00a0<\/span>\u00a0 \u03bc\u03b5<\/span> \"\textcolor{blue}{ \alpha, \beta \geq 0}\", \u00a0\u03b9\u03c3\u03c7\u03cd\u03b5\u03b9<\/span> <\/p>\n

  <\/span>   <\/span>\"\[\textcolor{blue}{\sqrt[v]{\alpha} \cdot \sqrt[v]{\beta}=\sqrt[v]{\alpha \cdot \beta}}\]\"<\/p>\n

<\/span><\/p>\n

\u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce<\/strong><\/a><\/span> \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7.<\/em><\/span><\/p>\n

\n

\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 5<\/strong>. N\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5<\/span> \"\textcolor{blue}{\alpha, \beta \in R}\" \u03bc\u03b5<\/span> \"\textcolor{blue}{\alpha \geq 0}\" \u03ba\u03b1\u03b9<\/span> \"\textcolor{blue}{\beta >0}\", \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9<\/span> <\/p>\n

  <\/span>   <\/span>\"\[\textcolor{blue}{\sqrt[v]{\dfrac{\alpha}{\beta}}=\dfrac{\sqrt[v]{\alpha}}{\sqrt[v]{\beta}}}\]\"<\/p>\n

\u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce<\/strong><\/a><\/span> \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7.<\/em><\/span><\/p>\n

\n

\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 6<\/strong>. \u0388\u03c3\u03c4\u03c9 \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 2\u03bf\u03c5 \u03b2\u03b1\u03b8\u03bc\u03bf\u03cd<\/span> \"\textcolor{blue}{\alpha x^2+\beta x+\gamma=0, \alpha \neq 0 }\" \u00a0\u03ba\u03b1\u03b9<\/span> \"\textcolor{blue}{x_1, x_2 }\" \u00a0\u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2. \u039d\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03bc\u03b1 \u03c4\u03c9\u03bd \u03c1\u03b9\u03b6\u03ce\u03bd S \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 \u03b7 \u03c3\u03c7\u03ad\u03c3\u03b7<\/span> <\/p>\n

  <\/span>   <\/span>\"\[\textcolor{blue}{S=x _1+ x _2=-\dfrac{\beta}{\alpha}}\]\"<\/p>\n

\u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce<\/strong> \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7.<\/em><\/span><\/p>\n

\n

\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 7<\/strong>. \u0388\u03c3\u03c4\u03c9 \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 2\u03bf\u03c5 \u03b2\u03b1\u03b8\u03bc\u03bf\u03cd<\/span> \"\textcolor{blue}{\alpha x^2+\beta x+\gamma=0, \alpha \neq 0}\" \u03ba\u03b1\u03b9<\/span> \"\textcolor{blue}{x_1, x_2}\" \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2. \u039d\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03bf \u03b3\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf \u03c4\u03c9\u03bd \u03c1\u03b9\u03b6\u03ce\u03bd P \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 \u03b7 \u03c3\u03c7\u03ad\u03c3\u03b7<\/span> <\/p>\n

  <\/span>   <\/span>\"\[\textcolor{blue}{P=x _1\cdot x _2=\dfrac{\gamma}{\alpha}}\]\"<\/p>\n

\u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce<\/strong> \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7.<\/em><\/span><\/p>\n

\n

\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 8<\/strong>. \u0388\u03c3\u03c4\u03c9 \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 2\u03bf\u03c5 \u03b2\u03b1\u03b8\u03bc\u03bf\u03cd<\/span> \"\textcolor{blue}{\alpha x^2+\beta x+\gamma=0, \alpha \neq 0}\" \u03ba\u03b1\u03b9<\/span> \"\textcolor{blue}{x_1, x_2 }\" \u03c1\u03af\u03b6\u03b5\u03c2 \u03c4\u03b7\u03c2 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7\u03c2. \u039d\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u00a0\u03bc\u03b5\u03c4\u03b1\u03c3\u03c7\u03b7\u03bc\u03b1\u03c4\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b7 \u03bc\u03bf\u03c1\u03c6\u03ae:<\/span> <\/p>\n

  <\/span>   <\/span>\"\[\textcolor{blue}{x^2-S x+P=0}\]\"<\/p>\n

\u03cc\u03c0\u03bf\u03c5<\/span> \u00a0S \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03ac\u03b8\u03c1\u03bf\u03b9\u03c3\u03bc\u03b1 \u03c4\u03c9\u03bd \u03c1\u03b9\u03b6\u03ce\u03bd \u03ba\u03b1\u03b9 P \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03b3\u03b9\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf \u03c4\u03bf\u03c5\u03c2.\u00a0<\/span><\/p>\n

\u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce<\/strong> \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7.<\/em><\/span><\/p>\n

\n

\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 9<\/strong>. \u039d\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03bf \u03bd\u03b9\u03bf\u03c3\u03c4\u03cc\u03c2 \u00a0\u03cc\u03c1\u03bf\u03c2 \u03bc\u03b9\u03b1\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03ae\u03c2 \u03c0\u03c1\u03bf\u03cc\u03b4\u03bf\u03c5 \u03bc\u03b5 \u03c0\u03c1\u03ce\u03c4\u03bf \u03cc\u03c1\u03bf <\/span>\"\textcolor{blue}{\alpha_1}\"\u00a0\u03ba\u03b1\u03b9 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03ac <\/span>\"\textcolor{blue}{\omeg }\" \u03b5\u03af\u03bd\u03b1\u03b9 <\/span><\/p>\n

  <\/span>   <\/span>\"\[\textcolor{blue}{ \alpha_\nu=\alpha_1+(\nu-1) \omega}\]\"<\/p>\n

.<\/p>\n

\u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce<\/strong> \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7.<\/em><\/span><\/p>\n

\n

\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 10. <\/span><\/strong>\u039d\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b1, \u03b2, \u03b3 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b4\u03b9\u03b1\u03b4\u03bf\u03c7\u03b9\u03ba\u03bf\u03af \u03cc\u03c1\u03bf\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03ae\u03c2 \u03c0\u03c1\u03bf\u03cc\u03b4\u03bf\u03c5 \u03b1\u03bd \u03ba\u03b1\u03b9 \u03bc\u03cc\u03bd\u03bf \u03b1\u03bd \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9<\/span> <\/p>\n

  <\/span>   <\/span>\"\[\textcolor{blue}{ \beta=\frac{\alpha+\gamma}{2}}\]\"<\/p>\n

\u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce<\/strong> \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7.<\/em><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 1. N\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \u00a0\u03b9\u03c3\u03c7\u03cd\u03b5\u03b9     \u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7. \u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 2. N\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \u00a0\u03ba\u03b1\u03b9 \u00a0 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9     \u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba \u03b5\u03b4\u03ce \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b5\u03b9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7. \u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 3. N\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9     \u039a\u03ac\u03bd\u03b5 \u03ba\u03bb\u03b9\u03ba…<\/p>\n","protected":false},"author":1,"featured_media":913,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17],"tags":[],"class_list":["post-857","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-17"],"featured_image_src":"https:\/\/gbelentzas.sites.sch.gr\/wp-content\/uploads\/2024\/05\/proofs.alyk_.alg_.jpeg","author_info":{"display_name":"admin","author_link":"https:\/\/gbelentzas.sites.sch.gr\/?author=1"},"yoast_head":"\n\u0395\u03ba\u03c6\u03c9\u03bd\u03ae\u03c3\u03b5\u03b9\u03c2 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c9\u03bd (\u0391 \u039b\u03c5\u03ba\u03b5\u03af\u03bf\u03c5) - MathsEdu.gr<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/gbelentzas.sites.sch.gr\/?p=857\" \/>\n<meta property=\"og:locale\" content=\"el_GR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0395\u03ba\u03c6\u03c9\u03bd\u03ae\u03c3\u03b5\u03b9\u03c2 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c9\u03bd (\u0391 \u039b\u03c5\u03ba\u03b5\u03af\u03bf\u03c5) - MathsEdu.gr\" \/>\n<meta property=\"og:description\" content=\"\u0391\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 1. 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