{"id":511,"date":"2012-12-07T23:42:55","date_gmt":"2012-12-07T14:42:55","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=511"},"modified":"2021-09-28T21:04:21","modified_gmt":"2021-09-28T12:04:21","slug":"thr200906","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr200906\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2009\uff1a\u7b2c6\u554f"},"content":{"rendered":"<hr \/>\n<p>\u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057\u3066, \\(x\\) \u306e\u65b9\u7a0b\u5f0f\r\n\\[\r\n| x(x-2) | +2a | x | -4a | x-2 | -1 = 0\r\n\\]\r\n\u304c, \u76f8\u7570\u306a\u308b \\(4\\) \u3064\u306e\u5b9f\u6570\u89e3\u3092\u3082\u3064\u3088\u3046\u306a \\(a\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p>\\[\\begin{align}\r\n| x(x-2) | +2a | x | & -4a | x-2 | -1 = 0 \\\\\r\n| x(x-2) | -1 & = 2a \\left( 2 | x-2 | - | x | \\right) \\quad ... [1]\r\n\\end{align}\\]\r\n[1] \u306e\u5de6\u8fba\u3068\u53f3\u8fba\u3092\u305d\u308c\u305e\u308c \\(f(x)\\) , \\(g(x)\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nf(x) & = \\left\\{ \\begin{array}{ll} x^2 -2x -1 & \\left( \\ x \\leqq 0 , 2 \\leqq x \\text{\u306e\u3068\u304d} \\right) \\\\ -x^2 +2x -1 & \\ \\left( \\ 0 \\lt x \\lt 2 \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right. , \\\\\r\ng(x) & = \\left\\{ \\begin{array}{ll} 2a (-x+4) & \\left( \\ x \\leqq 0 \\text{\u306e\u3068\u304d} \\right) \\\\ 2a(-3x+4) & \\left( \\ 0 \\lt x \\lt 2 \\text{\u306e\u3068\u304d} \\right) \\\\ 2a(x-4) & \\left( \\ x \\geqq 2 \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right.\r\n\\end{align}\\]\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(x \\leqq 0\\) \u306e\u3068\u304d\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tohoku_r_2009_06_01.png\" alt=\"\" title=\"tohoku_r_2009_06_01\" class=\"aligncenter size-full\" \/>\r\n\\(y = g(x)\\) \u306f, \u5b9a\u70b9 \\((4, 0)\\) \u3092\u901a\u308b\u50be\u304d \\(-2a\\) \u306e\u76f4\u7dda\u3067\u3042\u308b.<br \/>\r\n\u3053\u308c\u304c\u70b9 \\((0, -1)\\) \u3092\u901a\u308b\u306e\u306f\r\n\\[\\begin{align}\r\n-2a & = \\dfrac{1}{4} \\\\\r\n\\text{\u2234} \\quad a & = -\\dfrac{1}{8}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u3053\u306e\u7bc4\u56f2\u3067\u306e [1] \u306e\u5b9f\u6570\u89e3\u306e\u500b\u6570\u306f\r\n\\[\r\n\\left\\{ \\begin{array}{ll} 0 & \\left( \\ a \\lt -\\dfrac{1}{8} \\text{\u306e\u3068\u304d} \\right) \\\\ 1 & \\left( \\ a \\geqq -\\dfrac{1}{8} \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right.\r\n\\]<\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(0 \\lt x \\lt 2\\) \u306e\u3068\u304d\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tohoku_r_2009_06_02.png\" alt=\"\" title=\"tohoku_r_2009_06_02\" class=\"aligncenter size-full\" \/>\r\n\\(y = g(x)\\) \u306f, \u5b9a\u70b9 \\(\\left( \\dfrac{4}{3}, 0 \\right)\\) \u3092\u901a\u308b\u50be\u304d \\(-6a\\) \u306e\u76f4\u7dda\u3067\u3042\u308b.<br \/>\r\n\u3053\u306e\u76f4\u7dda\u304c\r\n<ol>\r\n<li><p><strong>[A]<\/strong>\u3000\u70b9 \\((0 , -1)\\) \u3092\u901a\u308b\u306e\u306f\r\n\\[\\begin{align}\r\n-6a & = \\dfrac{3}{4} \\\\\r\n\\text{\u2234} \\quad a &= -\\dfrac{1}{8}\r\n\\end{align}\\]<\/li>\r\n<li><p><strong>[B]<\/strong>\u3000\u70b9 \\((2 , -1)\\) \u3092\u901a\u308b\u306e\u306f\r\n\\[\\begin{align}\r\n-6a & = -\\dfrac{3}{2} \\\\\r\n\\text{\u2234} \\quad a & = \\dfrac{1}{4}\r\n\\end{align}\\]<\/li>\r\n<li><p><strong>[C]<\/strong>\u3000\\(y=f(x)\\) \u3068\u63a5\u3059\u308b\u306e\u306f, \u305d\u308c\u305e\u308c\u306e\u5f0f\u3088\u308a \\(y\\) \u3092\u6d88\u53bb\u3057\u3066\r\n\\[\\begin{align}\r\n-x^2 +2x -1 & = 2a(-3x+4) \\\\\r\nx^2 -2(3a+1)x +8a+1 & = 0 \\quad ... [2]\r\n\\end{align}\\]\r\n[2] \u306e\u5224\u5225\u5f0f \\(D _ 1\\) \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n\\dfrac{D _ 1}{4} = (3a+1)^2 & -(8a+1) = 0 \\\\\r\na (9a-2) & = 0 \\\\\r\n\\text{\u2234} \\quad a & = 0 , \\dfrac{2}{9}\r\n\\end{align}\\]\r\n\\(2\\) \u3064\u306e\u89e3\u306f\u3068\u3082\u306b [A] \u3068 [B] \u306e\u5834\u5408\u306e\u9593\u306b\u542b\u307e\u308c\u308b\u306e\u3067, \u63a5\u70b9\u306f \\(0 \\lt x \\lt 2\\) \u306e\u7bc4\u56f2\u306b\u3042\u308b.<\/p><\/li>\r\n<\/ol>\r\n\u3057\u305f\u304c\u3063\u3066, \u3053\u306e\u7bc4\u56f2\u3067\u306e [1] \u306e\u5b9f\u6570\u89e3\u306e\u500b\u6570\u306f\r\n\\[\r\n\\left\\{ \\begin{array}{ll} 1 & \\left( \\ a \\leqq -\\dfrac{1}{8} \\text{\u306e\u3068\u304d} \\right) \\\\ 2 & \\left( \\ -\\dfrac{1}{8} \\lt a \\lt 0 \\text{\u306e\u3068\u304d} \\right) \\\\ 1 & \\left( \\ a=0 \\text{\u306e\u3068\u304d} \\right) \\\\ 0 & \\left( \\ 0 \\lt a \\lt \\dfrac{2}{9} \\text{\u306e\u3068\u304d} \\right) \\\\ 1 & \\left( \\ a= \\dfrac{2}{9} \\text{\u306e\u3068\u304d} \\right) \\\\ 2 & \\left( \\ \\dfrac{2}{9} \\lt a \\lt \\dfrac{1}{4} \\text{\u306e\u3068\u304d} \\right) \\\\ 1 & \\left( \\ a \\geqq \\dfrac{1}{4} \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right.\r\n\\]<\/li>\r\n<li><p><strong>3*<\/strong>\u3000\\(x \\geqq 2\\) \u306e\u3068\u304d\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tohoku_r_2009_06_03.png\" alt=\"\" title=\"tohoku_r_2009_06_03\" class=\"aligncenter size-full\" \/>\r\n\\(y = g(x)\\) \u306f, \u5b9a\u70b9 \\((4, 0)\\) \u3092\u901a\u308b\u50be\u304d \\(2a\\) \u306e\u76f4\u7dda\u3067\u3042\u308b.<br \/>\r\n\u3053\u306e\u76f4\u7dda\u304c\r\n<ol>\r\n<li><p><strong>[A]<\/strong>\u3000\u70b9 \\((2, -1)\\) \u3092\u901a\u308b\u306e\u306f\r\n\\[\\begin{align}\r\n2a & = \\dfrac{1}{2} \\\\\r\n\\text{\u2234} \\quad a & = \\dfrac{1}{4}\r\n\\end{align}\\]<\/li>\r\n<li><p><strong>[B]<\/strong>\u3000\\(y=f(x)\\) \u3068\u63a5\u3059\u308b\u306e\u306f, \u305d\u308c\u305e\u308c\u306e\u5f0f\u3088\u308a \\(y\\) \u3092\u6d88\u53bb\u3057\u3066\r\n\\[\\begin{align}\r\nx^2 -2x -1 & = 2a(x-4) \\\\\r\nx^2 -2(a+1)x +8a-1 & = 0 \\quad ... [2]\r\n\\end{align}\\]\r\n[2] \u306e\u5224\u5225\u5f0f \\(D _ 2\\) \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\n\\dfrac{D _ 2}{4} = (a+1)^2 & -(8a-1) = 0 \\\\\r\na^2 -6a +2 & = 0 \\\\\r\n\\text{\u2234} \\quad a & = 3 \\pm \\sqrt{7}\r\n\\end{align}\\]\r\n\u3053\u306e\u3046\u3061, \u63a5\u70b9\u304c \\(x \\geqq 2\\) \u306b\u542b\u307e\u308c\u308b\u306e\u306f, \u50be\u304d\u304c\u5927\u304d\u3044\u65b9\u306a\u306e\u3067\r\n\\[\r\na = 3 +\\sqrt{7}\r\n\\]<\/li>\r\n<\/ol>\r\n\u3057\u305f\u304c\u3063\u3066, \u3053\u306e\u7bc4\u56f2\u3067\u306e [1] \u306e\u5b9f\u6570\u89e3\u306e\u500b\u6570\u306f\r\n\\[\r\n\\left\\{ \\begin{array}{ll} 1 & \\left( \\ a \\leqq \\dfrac{1}{4} \\text{\u306e\u3068\u304d} \\right) \\\\ 0 & \\left( \\ \\dfrac{1}{4} \\lt a \\lt 3+\\sqrt{7} \\text{\u306e\u3068\u304d} \\right) \\\\ 1 & \\left( \\ a = 3 +\\sqrt{7} \\text{\u306e\u3068\u304d} \\right) \\\\ 2 & \\left( \\ a \\gt 3+\\sqrt{7} \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right.\r\n\\]<\/li>\r\n<\/ol>\r\n<p><strong>1*<\/strong>\uff5e<strong>3*<\/strong>\u306e\u5834\u5408\u3092\u307e\u3068\u3081\u308b\u3068, [1] \u306e\u5b9f\u6570\u89e3\u306e\u500b\u6570 \\(N\\) \u306f\u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|ccccccccccc} a & \\cdots & -\\frac{1}{8} & \\cdots & 0 & \\cdots & \\frac{2}{9} & \\cdots & \\frac{1}{4} & \\cdots & 3 +\\sqrt{7} & \\cdots \\\\ \\hline \\hline \\mathbf{1^* } & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\\\ \\hline \\mathbf{2^* } & 1 & 1 & 2 & 1 & 0 & 1 & 2 & 1 & 1 & 1 & 1 \\\\ \\hline \\mathbf{3^* } & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 2 \\\\ \\hline \\hline N & 2 & 3 & 4 & 3 & 2 & 3 & 4 & 3 & 2 & 3 & 4 \\end{array}\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b \\(a\\) \u306e\u7bc4\u56f2\u306f\r\n\\[\r\n\\underline{-\\dfrac{1}{8} \\lt a \\lt 0 , \\ \\dfrac{2}{9} \\lt a \\lt \\dfrac{1}{4} , \\ 3+\\sqrt{7} \\lt a}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057\u3066, \\(x\\) \u306e\u65b9\u7a0b\u5f0f \\[ | x(x-2) | +2a | x | -4a | x-2 | -1 = 0 \\] \u304c, \u76f8\u7570\u306a\u308b \\(4\\) \u3064\u306e\u5b9f\u6570\u89e3\u3092\u3082\u3064\u3088\u3046\u306a \\(a\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081 &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/thr200906\/\">\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":[75],"tags":[148,15],"class_list":["post-511","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2009","tag-tohoku_r","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/511","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=511"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/511\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=511"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=511"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}