{"id":381,"date":"2012-04-22T18:49:20","date_gmt":"2012-04-22T09:49:20","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=381"},"modified":"2021-09-24T17:51:38","modified_gmt":"2021-09-24T08:51:38","slug":"tok201205","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok201205\/","title":{"rendered":"\u6771\u5de5\u59272012\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\\(A =\\left( \\begin{array}{cc} a & b \\\\ c & d \\end{array} \\right)\\) \u3067\u5b9a\u3081\u308b \\(1\\) \u6b21\u5909\u63db\u3092 \\(f\\) \u3068\u3059\u308b.\r\n\u539f\u70b9 O \\((0,0)\\) \u3068\u7570\u306a\u308b\u4efb\u610f\u306e \\(2\\) \u70b9 P, Q \u306b\u5bfe\u3057\u3066 \\(\\dfrac{\\text{OP'}}{\\text{OP}} =\\dfrac{\\text{OQ'}}{\\text{OQ}}\\) \u304c\u6210\u308a\u7acb\u3064.\r\n\u305f\u3060\u3057, P', Q' \u306f\u305d\u308c\u305e\u308c P, Q \u306e \\(f\\) \u306b\u3088\u308b\u50cf\u3092\u8868\u3059.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(a^2+c^2 =b^2+d^2\\) \u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(1\\) \u6b21\u5909\u63db \\(f\\) \u306b\u3088\u308a, \u70b9 \\((1, \\sqrt{3})\\) \u304c\u70b9 \\((-4,0)\\) \u306b\u79fb\u308b\u3068\u304d, \\(A\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    P, Q \u306f\u4efb\u610f\u306e\u70b9\u306a\u306e\u3067, P \\((1,0)\\) , Q \\((0,1)\\) \u3068\u304a\u3044\u3066\u3088\u3044.\r\n\\[\r\n\\text{OP} =\\text{OQ} =1\r\n\\]\r\n\u307e\u305f\r\n\\[\r\nA \\left( \\begin{array}{c} 1 \\\\ 0 \\end{array} \\right) = \\left( \\begin{array}{c} a \\\\ c \\end{array} \\right) , \\ A \\left( \\begin{array}{c} 0 \\\\ 1 \\end{array} \\right) = \\left( \\begin{array}{c} b \\\\ d \\end{array} \\right)\r\n\\]\r\n\u306a\u306e\u3067, P' \\((a,c)\\) , Q' \\((b,d)\\) .\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\n\\text{OP'} =\\sqrt{a^2+c^2} , \\ \\text{OQ'} =\\sqrt{b^2+d^2}\r\n\\]\r\n\u3053\u308c\u3089\u3092 \\(\\dfrac{\\text{OP'}}{\\text{OP}} =\\dfrac{\\text{OQ'}}{\\text{OQ}}\\) \u306b\u4ee3\u5165\u3057\u3066\r\n\\[\\begin{align}\r\n\\dfrac{\\sqrt{a^2+c^2}}{1} & = \\dfrac{\\sqrt{b^2+d^2}}{1} \\\\\r\n\\text{\u2234} \\quad a^2+c^2 & = b^2+d^2\r\n\\end{align}\\]\r\n

    (2)<\/strong><\/p>\r\n

    P \\((1, \\sqrt{3})\\) , P' \\((-4,0)\\) \u3068\u304a\u304f\u3068\r\n\\[\r\n\\dfrac{\\text{OP'}}{\\text{OP}} =\\dfrac{4}{\\sqrt{1+3}} =2\r\n\\]\r\n

    (1)<\/strong> \u306e\u7d50\u679c\u3068\u3042\u308f\u305b\u3066\r\n\\[\r\na^2+c^2 = b^2+d^2 = 4 \\quad ... [1]\r\n\\]\r\n\u307e\u305f\r\n\\[\r\nA \\left( \\begin{array}{c} 1 \\\\ \\sqrt{3} \\end{array} \\right) =\\left( \\begin{array}{c} a+\\sqrt{3} b \\\\ c+\\sqrt{3} d \\end{array} \\right)\r\n\\]\r\n\u306a\u306e\u3067, \u6761\u4ef6\u3088\u308a\r\n\\[\\begin{align}\r\na +\\sqrt{3} b & = -4 \\quad ... [2] \\\\\r\nc +\\sqrt{3} d & = 0 \\quad ... [3]\r\n\\end{align}\\]\r\n[2] [3] \u3092 [1] \u306b\u4ee3\u5165\u3059\u308c\u3070\r\n\\[\\begin{align}\r\n\\left( -\\sqrt{3} b -4 \\right)^2 +\\left( -\\sqrt{3} d \\right)^2 & = b^2 +d^2 = 2 \\\\\r\n3( b^2 +d^2 ) +8 \\sqrt{3} b +16 & = b^2 +d^2 =4 \\\\\r\n\\text{\u2234} \\quad b = \\dfrac{4 -12 -16 }{8 \\sqrt{3}} & = -\\sqrt{3}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, [1] \u3088\u308a\r\n\\[\r\nd =\\pm \\sqrt{4 -b^2} = \\pm 1\r\n\\]\r\n[2] \u3088\u308a\r\n\\[\r\na =-4 -\\sqrt{3} \\left( -\\sqrt{3} \\right) =-1\r\n\\]\r\n[3] \u3088\u308a\r\n\\[\r\nc = -\\sqrt{3} \\left( \\pm 1 \\right) = \\mp \\sqrt{3}\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\r\nA = \\underline{\\left( \\begin{array}{cc} -1 & -\\sqrt{3} \\\\ \\mp \\sqrt{3} & \\pm 1 \\end{array} \\right) \\quad ( \\text{\u8907\u53f7\u540c\u9806} )}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(A =\\left( \\begin{array}{cc} a & b \\\\ c & d \\end{array} \\right)\\) \u3067\u5b9a\u3081\u308b \\(1\\) \u6b21\u5909\u63db\u3092 \\(f\\) \u3068\u3059\u308b. \u539f\u70b9 O \\((0,0)\\) \u3068 … \u7d9a\u304d\u3092\u8aad\u3080 →<\/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":[61],"tags":[141,68],"class_list":["post-381","post","type-post","status-publish","format-standard","hentry","category-toko_2012","tag-toko","tag-68"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/381","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=381"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/381\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=381"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=381"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}