{"id":415,"date":"2012-06-02T11:53:03","date_gmt":"2012-06-02T02:53:03","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=415"},"modified":"2021-11-04T09:11:03","modified_gmt":"2021-11-04T00:11:03","slug":"htb201202","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201202\/","title":{"rendered":"\u4e00\u6a4b\u59272012\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(a\\) \u3092 \\(0\\) \u4ee5\u4e0a\u306e\u5b9a\u6570\u3068\u3059\u308b.\r\n\u95a2\u6570 \\(y = x^3-3a^2x\\) \u306e\u30b0\u30e9\u30d5\u3068\u65b9\u7a0b\u5f0f \\(|x|+|y| = 2\\) \u3067\u8868\u3055\u308c\u308b\u56f3\u5f62\u306e\u5171\u6709\u70b9\u306e\u500b\u6570\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\u4e0e\u3048\u3089\u308c\u305f\u30b0\u30e9\u30d5\u3068\u56f3\u5f62\u306f\u3068\u3082\u306b\u539f\u70b9\u306b\u3064\u3044\u3066\u5bfe\u79f0\u306a\u306e\u3067, \\(x \\geqq 0\\) \u306e\u90e8\u5206\u306b\u3064\u3044\u3066\u8003\u3048\u308c\u3070\u3088\u3044.<br \/>\r\n\\(y = x^3-3a^2x\\) ... [1] \u3068, \\(y =-x+2 \\ ( 0 \\leqq x \\leqq 2 )\\) ... [2] , \\(y = x-2 \\ ( 0 \\leqq x \\lt 2 )\\) ... [3] \u306e\u5171\u6709\u70b9\u306e\u500b\u6570\u306b\u3064\u3044\u3066\u8003\u3048\u308b.<br \/>\r\n[1] \u306b\u3064\u3044\u3066, \\(y = 0\\) \u3092\u3068\u304f\u3068\r\n\\[\\begin{align}\r\nx ( x -\\sqrt{3} a )( x +\\sqrt{3} a ) & =0 \\\\\r\n\\text{\u2234} \\quad x = 0 , \\sqrt{3} a &\r\n\\end{align}\\]\r\n\u307e\u305f\r\n\\[\r\ny' = 3x^2 -3a^2\r\n\\]\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000[1] \u304c\u70b9 \\((2,0)\\) \u3092\u901a\u308b\u3068\u304d\r\n\\[\\begin{align}\r\n0 & =2^3 -6a^2 \\\\\r\n\\text{\u2234} \\quad a & = \\dfrac{2 \\sqrt{3}}{3}\r\n\\end{align}\\]<\/li>\r\n<li><p><strong>2*<\/strong>\u3000[1] \u304c [3] \u3068\u63a5\u3059\u308b\u3068\u304d<br \/>\r\n\u63a5\u70b9\u306e \\(x\\) \u5ea7\u6a19\u3092 \\(t\\) \u3068\u304a\u3051\u3070, \u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\r\n\\[\\begin{align}\r\ny & = (3t^2 -3a^2)(x-t) +t^3 -3a^2t \\\\\r\n& = (3t^2 -3a^2) x -2t^3\r\n\\end{align}\\]\r\n\u3053\u308c\u304c [2] \u3068\u306a\u308b\u306e\u3067, \u4fc2\u6570\u3092\u6bd4\u8f03\u3057\u3066\r\n\\[\\begin{align}\r\n3t^2 -3a^2 =1 & , \\ -2t^3 =-2 \\\\\r\n\\text{\u2234} \\quad t = 1 & , \\ a = \\dfrac{\\sqrt{6}}{3}\r\n\\end{align}\\]<\/li>\r\n<\/ol>\r\n<p>\\(a\\) \u3092\u5909\u5316\u3055\u305b\u305f\u3068\u304d\u306e <strong>1*<\/strong> <strong>2*<\/strong> \u306e\u5834\u5408\u3092\u5883\u306b\u5171\u6709\u70b9\u306e\u500b\u6570\u306f\u5909\u5316\u3059\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/hitotsubashi_2012_02_01.png\" alt=\"hitotsubashi_2012_02_01\" class=\"aligncenter size-full\" \/>\r\n<p>\u3088\u3063\u3066, \u5bfe\u79f0\u6027\u3082\u8003\u616e\u3057\u3066, \u6c42\u3081\u308b\u5171\u6709\u70b9\u306e\u500b\u6570\u306f\r\n\\[\r\n\\underline{\\left\\{\\begin{array}{ll} 2 & \\left( \\ 0 \\lt a \\lt \\dfrac{\\sqrt{6}}{3} \\text{\u306e\u3068\u304d} \\right) \\\\ 4 & \\left( \\ a = \\dfrac{\\sqrt{6}}{3} \\text{\u306e\u3068\u304d} \\right) \\\\ 6 & \\left( \\ \\dfrac{\\sqrt{6}}{3} \\lt a \\lt \\dfrac{2 \\sqrt{3}}{3} \\text{\u306e\u3068\u304d} \\right) \\\\ 4 & \\left( \\ a = \\dfrac{2 \\sqrt{3}}{3} \\text{\u306e\u3068\u304d} \\right) \\\\ 2 & \\left( \\ a \\gt \\dfrac{2 \\sqrt{3}}{3} \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right.}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(a\\) \u3092 \\(0\\) \u4ee5\u4e0a\u306e\u5b9a\u6570\u3068\u3059\u308b. \u95a2\u6570 \\(y = x^3-3a^2x\\) \u306e\u30b0\u30e9\u30d5\u3068\u65b9\u7a0b\u5f0f \\(|x|+|y| = 2\\) \u3067\u8868\u3055\u308c\u308b\u56f3\u5f62\u306e\u5171\u6709\u70b9\u306e\u500b\u6570\u3092\u6c42\u3081\u3088.","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":[67],"tags":[146,68],"class_list":["post-415","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2012","tag-hitotsubashi","tag-68"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/415","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=415"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/415\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=415"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=415"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=415"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}