{"id":10669,"date":"2019-03-18T15:28:32","date_gmt":"2019-03-18T12:28:32","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=10669"},"modified":"2019-04-15T15:58:29","modified_gmt":"2019-04-15T12:58:29","slug":"problem-of-the-month-march-2019","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-march-2019\/","title":{"rendered":"Problem of the Month \u2013 March 2019"},"content":{"rendered":"<p>Find the minimal possible value of ab + bc + ac over all positive numbers a, b, c satisfying<br \/>\nabc = 1, a + b + c = 5 and<br \/>\n(ab + 2a + 2b \u2212 9)(bc + 2b + 2c \u2212 9)(ca + 2c + 2a \u2212 9) \u2265 0.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu Kawasaki, Japan<\/li>\n<li>Vedat Deveci Istanbul<\/li>\n<li>Ensar G\u00f6ktekin Malatya Anadolu Lisesi<\/li>\n<li>Hasan Z\u00fcbeyr Demir \u00d6zel Ankara \u00c7a\u011flayan Fen Lisesi<\/li>\n<li>Shin Min Hyeok Geoje Island, South Korea<\/li>\n<li>M. L\u00fctfi Yarar \u0130stanbul Technical University<\/li>\n<li>Albert Stadler Herrliberg, Switzerland<\/li>\n<li>Roushen Ovezmuradov Ashgabat, Turkmenistan<\/li>\n<li>Osman Asil Ege University, \u0130zmir<\/li>\n<li>Muhammet Habip Bing\u00f6l \u0130stanbul University<\/li>\n<li>Sten Hemmingsson Lund, Sweden<\/li>\n<li>Asude Ebrar K\u0131z\u0131lo\u011flu \u00d6zel Kad\u0131k\u00f6y E\u011fitmen Fen ve Anadolu Lisesi, \u0130stanbul<\/li>\n<li>\u0130rem Nur \u00c7evikcan Buca T\u0131rnakl\u0131 Fen Lisesi, \u0130zmir<\/li>\n<li>Sude Filiz \u0130zmir Bilfen Fen Lisesi<\/li>\n<li>Feray Lina Yence Buca T\u0131rnakl\u0131 Fen Lisesi, \u0130zmir<\/li>\n<li>Mahmut Sait Okyay UNIST, South Korea<\/li>\n<li>Berkay Unlu Dokuz Eyl\u00fcl University, \u0130zmir<\/li>\n<li>Max Nilsson Lund, Sweden<\/li>\n<li>Oktay Balk\u0131\u015f Aksaray Abd\u00fclhamid Han Fen Lisesi<\/li>\n<li>Animoku Abdulwahab Abuja, Nigeria<\/li>\n<li>Paolo Perfetti Universite degli studi di Tor Vergata Roma, Italy<\/li>\n<li>Henrik Aberg Gothenburg, Sweden<\/li>\n<li>Magnus Jakobsson Lund, Sweden<\/li>\n<li>Abdulkadir Tanr\u0131verdi Eski\u015fehir<\/li>\n<li>Vanio Beccaccioli Terni, Italy<\/li>\n<li>Roger Bengtsson Lund, Sweden<\/li>\n<li>B\u00fclent Do\u011fru Eski\u015fehir<\/li>\n<li>Johan Sandell Lund, Sweden<\/li>\n<li>Eren Can K\u0131z\u0131lda\u011f Massachusetts Ins\u0131tute of Technology, USA<\/li>\n<li>Dovran Nurgeldiyev Magtumguly Turkmen State University, Turkmenistan<\/li>\n<li>Metin Can Aydemir Bilkent University<\/li>\n<li>Berkay K\u0131rali<\/li>\n<li>Mustafa Serdar \u0130pek \u00dcsk\u00fcdar, Istanbul<\/li>\n<li>Alper Bahcekap\u0131l\u0131 Evrensel Fen Lisesi, Ankara<\/li>\n<li>Tu\u011f\u015fad Koyuncu Fethiye \u00d6mer \u00d6zyer Fen Lisesi<\/li>\n<li>Allan Druze Gulf Stream School Florida, USA<\/li>\n<\/ul>\n<ul>\n<li><strong>Solution:\u00a0<\/strong><a href=\"http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/1903a.pdf\">http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/1903a.pdf<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Find the minimal possible value of ab + bc + ac over all positive numbers a, b, c satisfying abc = 1, a + b + c = 5 and (ab + 2a + 2b \u2212 9)(bc + 2b + 2c \u2212 9)(ca + 2c + 2a \u2212 9) \u2265 [\u2026] <\/p>\n<div class=\"clear\"><\/div>\n<p><a class=\"more_link clearfix\" href=\"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-march-2019\/\" rel=\"nofollow\">Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-10669","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/10669","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/comments?post=10669"}],"version-history":[{"count":4,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/10669\/revisions"}],"predecessor-version":[{"id":10991,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/10669\/revisions\/10991"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=10669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}