{"id":69,"date":"2011-11-26T20:52:35","date_gmt":"2011-11-26T11:52:35","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=69"},"modified":"2021-11-04T09:29:25","modified_gmt":"2021-11-04T00:29:25","slug":"htb201101","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201101\/","title":{"rendered":"\u4e00\u6a4b\u59272011\uff1a\u7b2c1\u554f"},"content":{"rendered":"<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\u81ea\u7136\u6570 \\(x , y\\) \u306f, \\(1 \\lt x \\lt y\\) \u304a\u3088\u3073 \\(\\left( 1 +\\dfrac{1}{x} \\right) \\left( 1 +\\dfrac{1}{y} \\right) = \\dfrac{5}{3}\\) \u3092\u307f\u305f\u3059. \\(x , y\\) \u306e\u7d44\u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u81ea\u7136\u6570 \\(x , y , z\\) \u306f, \\(1 \\lt x \\lt y \\lt z\\) \u304a\u3088\u3073 \\(\\left( 1 +\\dfrac{1}{x} \\right) \\left( 1 +\\dfrac{1}{y} \\right) \\left( 1 +\\dfrac{1}{z} \\right) = \\dfrac{12}{5}\\) \u3092\u307f\u305f\u3059. \\(x , y , z\\) \u306e\u7d44\u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(x \\geqq 4\\) \u3068\u4eee\u5b9a\u3059\u308b\u3068,\r\n\\[\\begin{align}\r\n\\left( 1 +\\dfrac{1}{x} \\right) \\left( 1 +\\dfrac{1}{y} \\right) & \\leqq \\left( 1 +\\dfrac{1}{4} \\right) \\left( 1 +\\dfrac{1}{5} \\right) \\\\\r\n& = \\dfrac{3}{2} \\lt \\dfrac{5}{3}\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \u77db\u76fe\u3059\u308b.\r\n\u3057\u305f\u304c\u3063\u3066, \\(x=2 , 3\\) \u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308b.<\/p>\r\n<ul>\r\n<li><p>\\(x = 2\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n\\dfrac{3}{2} \\left( 1 +\\dfrac{1}{y} \\right) & = \\dfrac{5}{3} \\\\\r\n\\text{\u2234} \\quad y = 9 &\r\n\\end{align}\\]<\/li>\r\n<li><p>\\(x = 3\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n\\dfrac{4}{3} \\left( 1 +\\dfrac{1}{y} \\right) & = \\dfrac{5}{3} \\\\\r\n\\text{\u2234} \\quad y = 4 &\r\n\\end{align}\\]<\/li>\r\n<\/ul>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u7d44\u306f\r\n\\[\r\n( x , y ) = \\underline{( 2 , 9 ) , ( 3 , 4 )}\r\n\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\(x \\geqq 3\\) \u3068\u4eee\u5b9a\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n\\left( 1 +\\dfrac{1}{x} \\right) & \\left( 1 +\\dfrac{1}{y} \\right) \\left( 1 +\\dfrac{1}{z} \\right) \\\\\r\n& \\leqq \\left( 1 +\\dfrac{1}{3} \\right) \\left( 1 +\\dfrac{1}{4} \\right) \\left( 1 +\\dfrac{1}{5} \\right) \\\\\r\n& = 2 \\lt \\dfrac{12}{5}\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \u77db\u76fe\u3059\u308b.<br \/>\r\n\u3057\u305f\u304c\u3063\u3066, \\(x = 2\\) \u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308b.<br \/>\r\n\u3053\u306e\u3068\u304d\r\n\\[\\begin{align}\r\n\\dfrac{3}{2} \\left( 1 +\\dfrac{1}{y} \\right) \\left( 1 +\\dfrac{1}{z} \\right) & = \\dfrac{12}{5} \\\\\r\n\\left( 1 +\\dfrac{1}{y} \\right) \\left( 1 +\\dfrac{1}{z} \\right) & = \\dfrac{8}{5}\r\n\\end{align}\\]\r\n\u3053\u3053\u3067 \\(y \\geqq 5\\) \u3068\u4eee\u5b9a\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n\\left( 1 +\\dfrac{1}{y} \\right) \\left( 1 +\\dfrac{1}{z} \\right) & \\leqq \\left( 1 +\\dfrac{1}{5} \\right) \\left( 1 +\\dfrac{1}{6} \\right) \\\\\r\n& = \\dfrac{7}{5} \\lt \\dfrac{8}{5}\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \u77db\u76fe\u3059\u308b.<br \/>\r\n\u3057\u305f\u304c\u3063\u3066, \\(y=3 , 4\\) \u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308b.<\/p>\r\n<ul>\r\n<li><p>\\(y=3\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n\\dfrac{4}{3} \\left( 1 +\\dfrac{1}{z} \\right) & = \\dfrac{8}{5} \\\\\r\n\\text{\u2234} \\quad z = 5 &\r\n\\end{align}\\]<\/li>\r\n<li><p>\\(y=4\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\n\\dfrac{5}{4} \\left( 1 +\\dfrac{1}{z} \\right) & = \\dfrac{8}{5} \\\\\r\n\\text{\u2234} \\quad z = \\dfrac{25}{7} &\r\n\\end{align}\\]\r\n\u3053\u308c\u306f\u81ea\u7136\u6570\u3067\u306a\u3044\u306e\u3067\u4e0d\u9069.<\/p><\/li>\r\n<\/ul>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u7d44\u306f\r\n\\[\r\n( x , y , z ) = \\underline{( 2 , 3 , 5 )}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"(1)\u3000\u81ea\u7136\u6570 \\(x , y\\) \u306f, \\(1 \\lt x \\lt y\\) \u304a\u3088\u3073 \\(\\left( 1 +\\dfrac{1}{x} \\right) \\left( 1 +\\dfrac{1}{y} \\right) = \\ &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/htb201101\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[47],"tags":[146,13],"class_list":["post-69","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2011","tag-hitotsubashi","tag-13"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/69","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=69"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/69\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=69"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=69"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=69"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}