{"id":4782,"date":"2026-03-07T10:03:30","date_gmt":"2026-03-07T15:03:30","guid":{"rendered":"https:\/\/josmfs.net\/wordpress\/?p=4782"},"modified":"2026-03-07T10:03:30","modified_gmt":"2026-03-07T15:03:30","slug":"root-of-the-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2026\/03\/07\/root-of-the-problem\/","title":{"rendered":"Root of the Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-4779\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2026\/03\/Root-of-the-Problem-Fig2.jpg\" alt=\"\" width=\"201\" height=\"132\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2026\/03\/Root-of-the-Problem-Fig2.jpg 403w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2026\/03\/Root-of-the-Problem-Fig2-300x197.jpg 300w\" sizes=\"auto, (max-width: 201px) 100vw, 201px\" \/>This is a <a href=\"https:\/\/mindyourdecisions.com\/blog\/2026\/02\/26\/only-smart-minds-see-it-solve-for-the-value\/\">problem<\/a> from Presh Talwalkar.<\/p>\n<p>\u201cGiven that <em>x<\/em> satisfies the equation:<\/p>\n<p style=\"text-align: center;\"><em>x<\/em><sup>4<\/sup> + <em>x<\/em><sup>3<\/sup> + <em>x<\/em><sup>2<\/sup> + <em>x<\/em> + 1 = 0<\/p>\n<p>What is the value of<\/p>\n<p style=\"text-align: center;\">(<em>x<\/em><sup>33<\/sup> + 2\/<em>x<\/em><sup>22<\/sup>)(<em>x<\/em><sup>22<\/sup> + 3\/<em>x<\/em><sup>33<\/sup>)\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2026\/03\/Root-of-the-Problem-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2026\/03\/Root-of-the-Problem-260301.pdf\">Root of the Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a problem from Presh Talwalkar. \u201cGiven that x satisfies the equation: x4 + x3 + x2 + x + 1 = 0 What is the value of (x33 + 2\/x22)(x22 + 3\/x33)\u201d Answer. See Root of the Problem for solutions.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[133,17],"class_list":["post-4782","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-algebra","tag-presh-talwalkar"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4782","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=4782"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4782\/revisions"}],"predecessor-version":[{"id":4783,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4782\/revisions\/4783"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=4782"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=4782"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=4782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}