{"id":1282,"date":"2019-10-09T07:45:05","date_gmt":"2019-10-09T11:45:05","guid":{"rendered":"http:\/\/josmfs.net\/?p=1282"},"modified":"2019-10-09T07:45:05","modified_gmt":"2019-10-09T11:45:05","slug":"pairwise-products","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/10\/09\/pairwise-products\/","title":{"rendered":"Pairwise Products"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1280\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/10\/Pairwise-Products-Fig.jpg\" alt=\"\" width=\"200\" height=\"162\" \/>This 2005 four-star problem from Colin Hughes at <em>Maths Challenge<\/em> is also a bit challenging.<\/p>\n<p>\u201c<strong>Problem<\/strong><br \/>\nFor any set of real numbers, R = {x, y, z}, let sum of pairwise products,<br \/>\n<span style=\"color: #ffffff;\">________________<\/span>S = xy + xz + yz.<br \/>\nGiven that x + y + z = 1, prove that S \u2264 1\/3.\u201d<\/p>\n<p>Again, I took a different approach from Maths Challenge, whose solution began with an unexplained premise.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/10\/Pairwise-Products-190807.pdf\">Pairwise Products<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This 2005 four-star problem from Colin Hughes at Maths Challenge is also a bit challenging. \u201cProblem For any set of real numbers, R = {x, y, z}, let sum of pairwise products, ________________S = xy + xz + yz. Given that x + y + z = 1, prove that S \u2264 1\/3.\u201d Again, I [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[32,151,153],"class_list":["post-1282","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-calculus","tag-colin-hughes","tag-optimization"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1282","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=1282"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1282\/revisions"}],"predecessor-version":[{"id":1284,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1282\/revisions\/1284"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}