{"id":1116,"date":"2014-01-29T22:21:36","date_gmt":"2014-01-30T05:21:36","guid":{"rendered":"http:\/\/new-gro.dyn.hhhh.org\/joeboy\/blog\/?p=1116"},"modified":"2014-07-22T16:05:22","modified_gmt":"2014-07-22T23:05:22","slug":"mathematical-quickies-no-122","status":"publish","type":"post","link":"https:\/\/www.hhhh.org\/joeboy\/blog\/?p=1116","title":{"rendered":"Mathematical Quickies No.122"},"content":{"rendered":"<p>This problem kind of bugs me. Here is the problem and my first step:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1118\" title=\"Mathematical_Quickies_No122\" src=\"https:\/\/www.hhhh.org\/joeboy\/blog\/wp-content\/uploads\/2014\/01\/Mathematical_Quickies_No122.png\" alt=\"Mathematical Quickies No.122\" width=\"606\" height=\"202\" \/><\/p>\n<p>So I like my first step &#8211; but then my way of solving {a(a-1)(a-2)(a-3) = 120} is wonky. I want to expand it and use the quadratic equation &#8211; which\u00a0is not slick enough to\u00a0be what they are after. I am not seeing synthetic division, or any usual suspects &#8211; so I think I am missing something obvious.<\/p>\n<p>Rick, someone I work with, looked at the problem and immediately said you could tell that the solution needed to be divisible by 5, which happens to be a valid solution here. However I don&#8217;t believe that is always the case though.<\/p>\n<p>My way to get the solution shows a solution of {-2,5}. Work shown <a href=\"https:\/\/www.hhhh.org\/joeboy\/blog\/wp-content\/uploads\/2014\/01\/Mathematical_Quickies_No122.pdf\">here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This problem kind of bugs me. Here is the problem and my first step: So I like my first step &#8211; but then my way of solving {a(a-1)(a-2)(a-3) = 120} is wonky. I want to expand it and use the quadratic equation &#8211; which\u00a0is not slick enough to\u00a0be what they are after. I am not [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[40,12,59],"tags":[],"class_list":["post-1116","post","type-post","status-publish","format-standard","hentry","category-book-notes","category-problems","category-variable-substitutions"],"_links":{"self":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1116","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1116"}],"version-history":[{"count":19,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1116\/revisions"}],"predecessor-version":[{"id":1140,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1116\/revisions\/1140"}],"wp:attachment":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}