{"id":5484,"date":"2021-10-08T14:22:34","date_gmt":"2021-10-08T14:22:34","guid":{"rendered":"https:\/\/presswiki.allmath.gr\/wpwiki18\/?p=5484"},"modified":"2021-10-08T14:22:36","modified_gmt":"2021-10-08T14:22:36","slug":"%ce%b1%ce%bd%ce%b9%cf%83%cf%8c%cf%84%ce%b7%cf%84%ce%b1-andreescu","status":"publish","type":"post","link":"https:\/\/presswiki.allmath.gr\/wpwiki18\/2021\/10\/08\/14\/22\/34\/5484\/","title":{"rendered":"\u0391\u03bd\u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 Andreescu"},"content":{"rendered":"\n<figure class=\"wp-block-image\"><img src=\"https:\/\/latex.artofproblemsolving.com\/2\/6\/4\/264fff665becc96f5f9e05a178f2a31ee3f2603f.png\" alt=\"\\[\\frac{ a_1^2 } { b_1 } + \\frac{ a_2 ^2 } { b_2 } + \\cdots + \\frac{ a_n ^2 } { b_n } \\geq \\frac{ (a_1 + a_2 + \\cdots+ a_n ) ^2 } { b_1 + b_2 + \\cdots+ b_n }.\\]\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<p>\u0395\u03af\u03bd\u03b1\u03b9 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ae \u03ba\u03b1\u03b9 \u03c9\u03c2: T2 lemma, Engel&#8217;s form, or <a href=\"https:\/\/artofproblemsolving.com\/wiki\/index.php\/Titu%27s_Lemma\" data-type=\"URL\" data-id=\"https:\/\/artofproblemsolving.com\/wiki\/index.php\/Titu%27s_Lemma\">Sedrakyan&#8217;s inequality<\/a>.<\/p>\n\n\n\n<p>\u0391\u03bd\u03b1\u03c6\u03ad\u03c1\u03b5\u03c4\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03c9\u03c2 <a href=\"https:\/\/www.cut-the-knot.org\/m\/Algebra\/BergstromInequality.shtml\">Bergstrom&#8217;s Inequality<\/a> \u03bc\u03b5 \u03bc\u03af\u03b1 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7: <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img width=\"342\" height=\"191\" src=\"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-content\/uploads\/2021\/10\/\u03b5\u03b9\u03ba\u03cc\u03bd\u03b1-1.png\" alt=\"\" class=\"wp-image-5485\" srcset=\"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-content\/uploads\/2021\/10\/\u03b5\u03b9\u03ba\u03cc\u03bd\u03b1-1.png 342w, https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-content\/uploads\/2021\/10\/\u03b5\u03b9\u03ba\u03cc\u03bd\u03b1-1-300x168.png 300w\" sizes=\"(max-width: 342px) 85vw, 342px\" \/><\/figure>\n\n\n\n<p>\u03b7 \u03bf\u03c0\u03bf\u03af\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b9\u03c3\u03bf\u03b4\u03cd\u03bd\u03b1\u03bc\u03b7 \u03bc\u03b5 \u03c4\u03b7 \u03b6\u03b7\u03c4\u03bf\u03cd\u03bc\u03b5\u03bd\u03b7.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0395\u03af\u03bd\u03b1\u03b9 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ae \u03ba\u03b1\u03b9 \u03c9\u03c2: T2 lemma, Engel&#8217;s form, or Sedrakyan&#8217;s inequality. \u0391\u03bd\u03b1\u03c6\u03ad\u03c1\u03b5\u03c4\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03c9\u03c2 Bergstrom&#8217;s Inequality \u03bc\u03b5 \u03bc\u03af\u03b1 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7: \u03b7 \u03bf\u03c0\u03bf\u03af\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b9\u03c3\u03bf\u03b4\u03cd\u03bd\u03b1\u03bc\u03b7 \u03bc\u03b5 \u03c4\u03b7 \u03b6\u03b7\u03c4\u03bf\u03cd\u03bc\u03b5\u03bd\u03b7.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[17,62],"tags":[100],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts\/5484"}],"collection":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/comments?post=5484"}],"version-history":[{"count":1,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts\/5484\/revisions"}],"predecessor-version":[{"id":5486,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/posts\/5484\/revisions\/5486"}],"wp:attachment":[{"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/media?parent=5484"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/categories?post=5484"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/presswiki.allmath.gr\/wpwiki18\/wp-json\/wp\/v2\/tags?post=5484"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}