{"id":217,"date":"2011-12-03T00:11:14","date_gmt":"2011-12-02T15:11:14","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=217"},"modified":"2021-11-04T13:12:07","modified_gmt":"2021-11-04T04:12:07","slug":"htb200903","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb200903\/","title":{"rendered":"\u4e00\u6a4b\u59272009\uff1a\u7b2c3\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(p , q\\) \u3092\u5b9f\u6570\u3068\u3059\u308b.\r\n\u653e\u7269\u7dda \\(y = x^2-2px+q\\) \u304c, \u4e2d\u5fc3 \\((p, 2p)\\) \u3067\u534a\u5f84 \\(1\\) \u306e\u5186\u3068\u4e2d\u5fc3 \\((p, p)\\) \u3067\u534a\u5f84 \\(1\\) \u306e\u5186\u306e\u4e21\u65b9\u3068\u5171\u6709\u70b9\u3092\u3082\u3064. \u3053\u306e\u653e\u7269\u7dda\u306e\u9802\u70b9\u304c\u5b58\u5728\u3057\u3046\u308b\u9818\u57df\u3092 \\(xy\\) \u5e73\u9762\u4e0a\u306b\u56f3\u793a\u305b\u3088.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\u653e\u7269\u7dda\u306e\u9802\u70b9\u3092 \\(( X, Y )\\) \u3068\u304a\u304f.\r\n\\[\r\ny = x^2 -2px +q = (x-p)^2-p^2+q\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nX = p & , \\ Y = -p^2+q \\\\\r\n\\text{\u2234} \\quad p = X & , \\ q = X^2+Y \\quad ... [1]\r\n\\end{align}\\]\r\n\u653e\u7269\u7dda\u306e\u9802\u70b9, \u5186\u306e\u4e2d\u5fc3\u304c\u3059\u3079\u3066 \\(x=p\\) \u4e0a\u306b\u3042\u308b\u3053\u3068\u304b\u3089, \\(y = x^2\\) \u3068 \\(y\\) \u8ef8\u306b\u4e2d\u5fc3\u3092\u3082\u3064\u534a\u5f84 \\(1\\) \u306e\u5186\u304c\u5171\u6709\u70b9\u3092\u3082\u3064\u305f\u3081\u306e\u653e\u7269\u7dda\u306e\u9802\u70b9\u3068, \u5186\u306e\u4e2d\u5fc3\u306e\u8ddd\u96e2 \\(h\\) \u306b\u3064\u3044\u3066\u306e\u6761\u4ef6\u3092\u8003\u3048\u308c\u3070\u3088\u3044.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\u5186\u304c\u653e\u7269\u7dda\u3088\u308a\u4e0b\u5074\u306b\u3042\u308b\u3068\u304d<br \/>\r\n\u660e\u3089\u304b\u306b, \\(h \\leqq 1\\) .<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\u5186\u304c\u653e\u7269\u7dda\u3088\u308a\u4e0a\u5074\u306b\u3042\u308b\u3068\u304d\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/hitotsubashi_200903_01.png\" alt=\"hitotsubashi_200903_01\" class=\"aligncenter size-full\" \/>\r\n\\(h\\) \u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f\u4e0a\u56f3\u306e\u3088\u3046\u306b, \u5186\u3068\u653e\u7269\u7dda\u304c \\(x\\) \u5ea7\u6a19\u304c \\(t \\ ( 0 \\lt t \\lt 1 )\\) \u306e\u70b9\u3067\u63a5\u3059\u308b\u3068\u304d\u3067\u3042\u308b.<br \/>\r\n\\(y' = 2x\\) \u3088\u308a, \u3053\u306e\u70b9\u3067\u306e\u6cd5\u7dda\u306e\u50be\u304d\u306f \\(-\\dfrac{1}{2t}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\nt^2 & +\\left( \\dfrac{1}{2} \\right)^2 = 1^2 \\\\\r\n\\text{\u2234} \\quad t & = \\dfrac{\\sqrt{3}}{2}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\nh \\leqq \\left( \\dfrac{\\sqrt{3}}{2} \\right)^2 +\\dfrac{1}{2} = \\dfrac{5}{4}\r\n\\]<\/li>\r\n<\/ol>\r\n<p><strong>1*<\/strong> <strong>2*<\/strong> \u3088\u308a, \u6c42\u3081\u308b\u6761\u4ef6\u306f [1] \u3082\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n& \\left\\{ \\begin{array}{l} Y-1 \\leqq X \\leqq Y+\\dfrac{5}{4} \\\\ Y-1 \\leqq 2 (X^2+Y) \\leqq Y+\\dfrac{5}{4} \\end{array} \\right. \\\\\r\n\\text{\u2234} \\quad & \\left\\{ \\begin{array}{l} X-\\dfrac{5}{4} \\leqq Y \\leqq X+1 \\\\ -2X^2-1 \\leqq Y \\leqq -2X^2+\\dfrac{5}{4} \\end{array} \\right.\r\n\\end{align}\\]\r\n\u3053\u306e\u9818\u57df\u3092\u56f3\u793a\u3059\u308c\u3070\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u3092\u542b\u3080\uff09.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/hitotsubashi_200903_02.png\" alt=\"hitotsubashi_200903_02\" class=\"aligncenter size-full\" \/>\r\n","protected":false},"excerpt":{"rendered":"\\(p , q\\) \u3092\u5b9f\u6570\u3068\u3059\u308b. \u653e\u7269\u7dda \\(y = x^2-2px+q\\) \u304c, \u4e2d\u5fc3 \\((p, 2p)\\) \u3067\u534a\u5f84 \\(1\\) \u306e\u5186\u3068\u4e2d\u5fc3 \\((p, p)\\) \u3067\u534a\u5f84 \\(1\\) \u306e\u5186\u306e\u4e21\u65b9\u3068\u5171\u6709\u70b9\u3092\u3082\u3064. \u3053 &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/htb200903\/\">\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":[45],"tags":[146,15],"class_list":["post-217","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2009","tag-hitotsubashi","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/217","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=217"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/217\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=217"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=217"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}