{"id":599,"date":"2013-02-02T07:48:03","date_gmt":"2013-02-01T22:48:03","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=599"},"modified":"2021-03-18T15:22:36","modified_gmt":"2021-03-18T06:22:36","slug":"tkr200703","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr200703\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2007\uff1a\u7b2c3\u554f"},"content":{"rendered":"<hr \/>\n<p>\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(2\\) \u70b9 P , Q \u304c, \u66f2\u7dda \\(y=x^2 \\ ( -1 \\leqq x \\leqq 1 )\\) \u4e0a\u3092\u81ea\u7531\u306b\u52d5\u304f\u3068\u304d,\r\n\u7dda\u5206 PQ \u3092 \\(1 : 2\\) \u306b\u5185\u5206\u3059\u308b\u70b9 R \u304c\u52d5\u304f\u7bc4\u56f2\u3092 \\(D\\) \u3068\u3059\u308b.\r\n\u305f\u3060\u3057, \\(\\text{P} = \\text{Q}\\) \u306e\u3068\u304d\u306f \\(\\text{R} = \\text{P}\\) \u3068\u3059\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(a\\) \u3092 \\(-1 \\leqq a \\leqq 1\\) \u3092\u307f\u305f\u3059\u5b9f\u6570\u3068\u3059\u308b\u3068\u304d,\r\n\u70b9 \\((a,b)\\) \u304c \\(D\\) \u306b\u5c5e\u3059\u308b\u305f\u3081\u306e \\(b\\) \u306e\u6761\u4ef6\u3092 \\(a\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(D\\) \u3092\u56f3\u793a\u305b\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>P \\(( p, p^2 )\\) , Q \\(( q, q^2 )\\) \\(( -1 \\leqq p \\leqq 1 , -1 \\leqq q \\leqq 1\\ \\ ... [1] ) \\) \u3068\u304a\u304f.<br \/>\r\n\u3053\u306e\u3068\u304d\r\n\\[\\begin{align}\r\na & = \\dfrac{2p+q}{3} \\quad ... [2] \\\\\r\nb & = \\dfrac{2p^2+q^2}{3} \\quad ... [3]\r\n\\end{align}\\]\r\n[2] \u3088\u308a, \\(q = 3a-2p\\) \u306a\u306e\u3067, [3] \u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\r\n3b = 2p^2 +( 3a-2p )^2\r\n\\]\r\n\u3086\u3048\u306b\r\n\\[\\begin{align}\r\nb & = 3a^2 -4pa +2p^2 \\\\\r\n& = 2(p-a)^2 +a^2 \\geqq a^2\r\n\\end{align}\\]\r\n\u307e\u305f, [1] \u3088\u308a\r\n\\[\\begin{align}\r\n& -1 \\leqq 3a-2p \\leqq 1 \\\\\r\n\\text{\u2234} \\quad & \\dfrac{3a-1}{2} \\leqq p \\leqq \\dfrac{3a+1}{2} \\quad ... [4]\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(b = f(p)\\) \u3068\u304a\u3044\u3066, [1] \u304b\u3064 [4] \u306b\u304a\u3044\u3066\u53d6\u308a\u5f97\u308b\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u308c\u3070\u3088\u3044.<br \/>\r\n\u6700\u5c0f\u5024, \u6700\u5927\u5024\u306e\u5019\u88dc\u306f<\/p>\r\n<ul>\r\n<li><p>\\(f(a) = a^2\\)<br \/>\r\n\uff08\u305f\u3060\u3057, \u6700\u5c0f\u5024\u306b\u306e\u307f\u306a\u308a\u3048\u308b\uff09<\/p><\/li>\r\n<li><p>\\(f(-1) = 3a^2+4a+2 = 3 \\left( a +\\dfrac{2}{3} \\right)^2 +\\dfrac{2}{3}\\)<br \/>\r\n\uff08\u305f\u3060\u3057, \\(\\dfrac{3a-1}{2} \\leqq -1 \\leqq \\dfrac{3a+1}{2}\\) \u3059\u306a\u308f\u3061 \\(-1 \\leqq a -\\dfrac{1}{3}\\) \u306e\u3068\u304d\u306e\u307f\uff09<\/p><\/li>\r\n<li><p>\\(f(1) = 3a^2-4a+2 = 3 \\left( a -\\dfrac{2}{3} \\right)^2 +\\dfrac{2}{3}\\)<br \/>\r\n\uff08\u305f\u3060\u3057, \\(\\dfrac{3a-1}{2} \\leqq 1 \\leqq \\dfrac{3a+1}{2}\\) \u3059\u306a\u308f\u3061 \\(\\dfrac{1}{3} \\leqq a \\leqq 1\\) \u306e\u3068\u304d\u306e\u307f\uff09<\/p><\/li>\r\n<li><p>\\(f \\left( \\dfrac{3a-1}{2} \\right) = \\dfrac{3 a^2}{2} -a+\\dfrac{1}{2} = \\dfrac{3}{2} \\left( a -\\dfrac{1}{3} \\right)^2 +\\dfrac{1}{3}\\)<br \/>\r\n\uff08\u305f\u3060\u3057, \\(-1 \\leqq \\dfrac{3a-1}{2} \\leqq 1\\) \u3059\u306a\u308f\u3061 \\(-\\dfrac{1}{3} \\leqq a \\leqq 1\\) \u306e\u3068\u304d\u306e\u307f\uff09<\/p><\/li>\r\n<li><p>\\(f \\left( \\dfrac{3a+1}{2} \\right) = \\dfrac{3 a^2}{2} +a+\\dfrac{1}{2} = \\dfrac{3}{2} \\left( a +\\dfrac{1}{3} \\right)^2 +\\dfrac{1}{3}\\)<br \/>\r\n\uff08\u305f\u3060\u3057, \\(-1 \\leqq \\dfrac{3a+1}{2} \\leqq 1\\) \u3059\u306a\u308f\u3061 \\(-1 \\leqq a \\leqq \\dfrac{1}{3}\\) \u306e\u3068\u304d\u306e\u307f\uff09<\/p><\/li>\r\n<\/ul>\r\n<p>\u4ee5\u4e0a\u306e\u5019\u88dc\u306e\u5927\u5c0f\u3092\u6bd4\u8f03\u3059\u308c\u3070<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tokyo_r_2007_03_01.png\" alt=\"tokyo_r_2007_03_01\" class=\"aligncenter size-full\" \/>\r\n<p>\\[\r\n\\underline{\\left\\{ \\begin{array}{ll} a^2 \\leqq b \\leqq 3a^2+4a+2 & \\left( -1 \\leqq a \\lt -\\dfrac{1}{3} \\ \\text{\u306e\u3068\u304d} \\right) \\\\ a^2 \\leqq b \\leqq \\dfrac{3 a^2}{2} +a+\\dfrac{1}{2} & \\left( -\\dfrac{1}{3} \\leqq a \\lt 0 \\ \\text{\u306e\u3068\u304d} \\right) \\\\ a^2 \\leqq b \\leqq \\dfrac{3 a^2}{2} -a+\\dfrac{1}{2} & \\left( 0 \\leqq a \\lt \\dfrac{1}{3} \\ \\text{\u306e\u3068\u304d} \\right) \\\\ a^2 \\leqq b \\leqq 3a^2-4a+2 & \\left( \\dfrac{1}{3} \\leqq a \\leqq 1 \\ \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right.}\r\n\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p><strong>(1)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u542b\u3080\uff09.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tokyo_r_2007_03_02.png\" alt=\"tokyo_r_2007_03_02\" class=\"aligncenter size-full\" \/>\r\n","protected":false},"excerpt":{"rendered":"\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(2\\) \u70b9 P , Q \u304c, \u66f2\u7dda \\(y=x^2 \\ ( -1 \\leqq x \\leqq 1 )\\) \u4e0a\u3092\u81ea\u7531\u306b\u52d5\u304f\u3068\u304d, \u7dda\u5206 PQ \u3092 \\(1 : 2\\) \u306b\u5185\u5206\u3059\u308b\u70b9 R \u304c\u52d5\u304f\u7bc4\u56f2\u3092 \\(D &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tkr200703\/\">\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":[85],"tags":[139,109],"class_list":["post-599","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2007","tag-tokyo_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/599","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=599"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/599\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=599"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=599"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=599"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}