{"id":184,"date":"2011-12-02T22:54:10","date_gmt":"2011-12-02T13:54:10","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=184"},"modified":"2021-09-10T20:48:14","modified_gmt":"2021-09-10T11:48:14","slug":"tok200902","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok200902\/","title":{"rendered":"\u6771\u5de5\u59272009\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057, \u6b21\u306e \\(1\\) \u6b21\u5909\u63db\r\n\\[\r\nf(x,y) = \\left( ax+(a-2)y , (a-2)x+ay \\right)\r\n\\]\r\n\u3092\u8003\u3048\u308b. \u4ee5\u4e0b\u306e \\(2\\) \u6761\u4ef6\u3092\u307f\u305f\u3059\u76f4\u7dda \\(L\\) \u304c\u5b58\u5728\u3059\u308b\u3088\u3046\u306a \\(a\\) \u3092\u6c42\u3081\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(L\\) \u306f\u70b9 \\((0, 1)\\) \u3092\u901a\u308b.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u70b9 \\(Q\\) \u304c \\(L\\) \u4e0a\u306b\u3042\u308c\u3070, \u305d\u306e \\(f\\) \u306b\u3088\u308b \\(f(Q)\\) \u3082 \\(L\\) \u4e0a\u306b\u3042\u308b.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\\(1\\) \u6b21\u5909\u63db \\(f\\) \u306b\u5bfe\u5fdc\u3059\u308b\u884c\u5217\u306f\r\n\\[\r\n\\left( \\begin{array}{cc} a & a-2 \\\\ a-2 & a \\end{array} \\right)\r\n\\]\r\n\\(L\\) \u306f, <strong>1*<\/strong> \\(x = 0\\) , <strong>2*<\/strong> \\(y = kx+1\\) \uff08 \\(k\\) \u306f\u5b9f\u6570\uff09\u306e \\(2\\) \u3064\u306e\u5834\u5408\u304c\u8003\u3048\u3089\u308c\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(x = 0\\) \u306e\u3068\u304d<br \/>\r\n\\(L\\) \u4e0a\u306e\u70b9\u306f \\(( 0 , t )\\) \u3068\u8868\u305b, \u3053\u308c\u3092 \\(f\\) \u3067\u5909\u63db\u3059\u308b\u3068\r\n\\[\r\n\\left( \\begin{array}{cc} a & a-2 \\\\ a-2 & a \\end{array} \\right) \\left( \\begin{array}{c} 0 \\\\ t \\end{array} \\right) = \\left( \\begin{array}{c} (a-2)t \\\\ at \\end{array} \\right)\r\n\\]\r\n\u3053\u306e\u70b9\u304c \\(x = 0\\) \u4e0a\u306b\u3042\u308b\u306e\u3067\r\n\\[\r\n(a-2) t = 0\r\n\\]\r\n\u3053\u308c\u304c \\(t\\) \u306b\u3088\u3089\u305a\u6210\u7acb\u3059\u308b\u306e\u3067\r\n\\[\\begin{align}\r\na-2 & = 0 \\\\\r\n\\text{\u2234} \\quad a & = 2\r\n\\end{align}\\]<\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(y = kx+1\\) \u306e\u3068\u304d<br \/>\r\n\\(L\\) \u4e0a\u306e\u70b9\u306f \\(( t , kt+1 )\\) \u3068\u8868\u305b, \u3053\u308c\u3092 \\(f\\) \u3067\u5909\u63db\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n\\left( \\begin{array}{cc} a & a-2 \\\\ a-2 & a \\end{array} \\right) \\left( \\begin{array}{c} t \\\\ kt+1 \\end{array} \\right) & = \\left( \\begin{array}{c} at +(a-2)(kt+1) \\\\ (a-2)t+a(kt+1) \\end{array} \\right) \\\\\r\n& = \\left( \\begin{array}{c} \\{ k(a-2)+a \\}t+a-2 \\\\ (ka+a-2)t+a \\end{array} \\right)\r\n\\end{align}\\]\r\n\u3053\u306e\u70b9\u304c \\(y = kx+1\\) \u4e0a\u306b\u3042\u308b\u306e\u3067\r\n\\[\\begin{align}\r\n(ka+a-2) t +a = k \\{ k(a-2)+a \\} t & +k(a-2) +1 \\\\\r\n(k^2-1)(a-2)t -k(a-2) +a-1 & = 0\r\n\\end{align}\\]\r\n\u3053\u308c\u304c \\(t\\) \u306b\u3088\u3089\u305a\u6210\u7acb\u3059\u308b\u306e\u3067\r\n\\[\r\n\\left\\{ \\begin{array}{ll} (k^2-1)(a-2)=0 & \\quad ... [1] \\\\ -k(a-2) +a-1=0 & \\quad ... [2] \\end{array} \\right.\r\n\\]\r\n[1] \u3088\u308a\r\n\\[\r\na = 2 \\ \\text{\u307e\u305f\u306f} \\ k = \\pm 1\r\n\\]\r\n<ul>\r\n<li><p>\\(a = 2\\) \u306e\u3068\u304d, [2] \u304c\u6210\u7acb\u3057\u306a\u3044\u306e\u3067\u4e0d\u9069.<\/p><\/li>\r\n<li><p>\\(k = 1\\) \u306e\u3068\u304d, [2] \u304c\u6210\u7acb\u3057\u306a\u3044\u306e\u3067\u4e0d\u9069.<\/p><\/li>\r\n<li><p>\\(k = -1\\) \u306e\u3068\u304d, [2] \u3088\u308a\r\n\\[\\begin{align}\r\n2a-3 & = 0 \\\\\r\n\\text{\u2234} \\quad a & = \\dfrac{3}{2}\r\n\\end{align}\\]<\/li>\r\n<\/ul><\/li>\r\n<\/ol>\r\n<p><strong>1*<\/strong> <strong>2*<\/strong> \u3088\u308a, \u6c42\u3081\u308b \\(a\\) \u306e\u5024\u306f\r\n\\[\r\na= \\underline{\\dfrac{3}{2} , 2}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057, \u6b21\u306e \\(1\\) \u6b21\u5909\u63db \\[ f(x,y) = \\left( ax+(a-2)y , (a-2)x+ay \\right) \\] \u3092\u8003\u3048\u308b. \u4ee5\u4e0b\u306e \\(2\\) \u6761\u4ef6\u3092\u307f\u305f\u3059\u76f4\u7dda \\(L\\)  &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tok200902\/\">\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":[24],"tags":[141,15],"class_list":["post-184","post","type-post","status-publish","format-standard","hentry","category-toko_2009","tag-toko","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/184","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=184"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/184\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=184"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=184"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=184"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}