{"id":1851,"date":"2021-09-05T20:41:22","date_gmt":"2021-09-05T11:41:22","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1851"},"modified":"2021-09-08T13:16:22","modified_gmt":"2021-09-08T04:16:22","slug":"ngr201601","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr201601\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2016\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\u66f2\u7dda \\(y = x^2\\) \u4e0a\u306b \\(2\\) \u70b9 A \\(( -2 , 4 )\\) , B \\(( b , b^2 )\\) \u3092\u3068\u308b. \u305f\u3060\u3057 \\(b \\gt -2\\) \u3068\u3059\u308b. \u3053\u306e\u3068\u304d, \u6b21\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059 \\(b\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p>\r\n

    \r\n
  1. \u6761\u4ef6\uff1a \\(y = x^2\\) \u4e0a\u306e\u70b9 T \\(( t , t^2 ) \\ ( -2 \\lt t \\lt b )\\) \u3067, \\(\\angle \\text{ATB}\\) \u304c\u76f4\u89d2\u306b\u306a\u308b\u3082\u306e\u304c\u5b58\u5728\u3059\u308b.<\/li>\r\n<\/ol>\r\n
    \r\n\r\n

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

    A , B , T \u306f\u4e92\u3044\u306b\u7570\u306a\u308b\u70b9\u3067,\r\n\\[\\begin{align}\r\n\\text{AT \u306e\u50be\u304d} & = \\dfrac{t^2 -4}{t+2} = t-2 \\ , \\\\\r\n\\text{BT \u306e\u50be\u304d} & = \\dfrac{t^2 -b^2}{t-b} = t+b \\ .\r\n\\end{align}\\]\r\nAT \u3068 BT \u304c\u76f4\u4ea4\u3059\u308b\u306e\u3067\r\n\\[\\begin{align}\r\n( t-2 ) ( t+b ) & = -1 \\\\\r\nt^2 +(b-2) t -2b +1 & = 0 \\quad ... [1] \\ .\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(t\\) \u306e\u65b9\u7a0b\u5f0f [1] \u304c, \\(-2 \\lt t \\lt b\\) \u306b\u89e3\u3092\u3082\u3064\u305f\u3081\u306e \\(b\\) \u306e\u6761\u4ef6\u3092\u6c42\u3081\u308c\u3070\u3088\u3044.
    \r\n[1] \u306e\u5de6\u8fba\u3092 \\(f(t)\\) \u3068\u304a\u304f\u3068, \\(y = f(t)\\) \u306f, \u4e0b\u306b\u51f8\u3067, \u76f4\u7dda \\(t = 1 -\\dfrac{b}{2}\\) \u3092\u8ef8\u306b\u3082\u3064\u653e\u7269\u7dda\u3067\u3042\u308b.
    \r\n\u307e\u305f\r\n\\[\\begin{align}\r\nf(-2) & = 4 -2(b-2) -2b +1 \\\\\r\n& = -4b +9 \\ , \\\\\r\nf(b) & = b^2 +(b-2)b -2b +1 \\\\\r\n& = 2b^2 -4b +1 \\ .\r\n\\end{align}\\]\r\n\u6c42\u3081\u308b\u6761\u4ef6\u306f, \u4e0b\u306e 1*<\/strong> , 2*<\/strong> \u306e\u3044\u305a\u308c\u304b\u306e\u3068\u304d\u3067\u3042\u308b.<\/p>\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(f(-2) f(b) \\lt 0 \\ ... [2]\\) .<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000[1] \u306e\u5224\u5225\u5f0f \\(D\\) \u306b\u3064\u3044\u3066\uff1a \\(D \\geqq 0 \\ ... [3]\\) , \u8ef8\u306e\u4f4d\u7f6e\u306b\u3064\u3044\u3066\uff1a \\(-2 \\lt 1 -\\dfrac{b}{2} \\lt b \\ ... [4]\\) , \\(f(-2) \\geqq 0 \\ ... [5]\\) , \\(f(b) \\geqq 0 \\ ... [6]\\) \uff08\u305f\u3060\u3057, \\(f(-2) = f(b) = 0 \\ ... [7] \\) \u306e\u5834\u5408\u3092\u9664\u304f\uff09.<\/p><\/li>\r\n

    3. 1*<\/strong> \u306b\u3064\u3044\u3066
      \r\n[2] \u3088\u308a\r\n\\[\\begin{align}\r\n( -4b +9 ) ( 2b^2 -4b +1 ) & \\lt 0 \\\\\r\n\\left( b -\\dfrac{9}{4} \\right) \\left\\{ b -\\left( 1 -\\dfrac{\\sqrt{2}}{2} \\right) \\right\\} \\left\\{ b -\\left( 1 +\\dfrac{\\sqrt{2}}{2} \\right) \\right\\} & \\gt 0 \\\\\r\n\\text{\u2234} \\quad 1 -\\dfrac{\\sqrt{2}}{2} \\lt b \\lt 1 +\\dfrac{\\sqrt{2}}{2} & , \\ \\dfrac{9}{4} \\lt b \\ .\r\n\\end{align}\\]<\/li>\r\n

    4. 2*<\/strong> \u306b\u3064\u3044\u3066
      \r\n[3] \u3088\u308a\r\n\\[\\begin{align}\r\nD & = (b-2)^2 +4 (2b-1) \\\\\r\n& = b (b+4) \\geqq 0 \\\\\r\n\\text{\u2234} \\quad b & \\geqq 0 \\quad ( \\ \\text{\u2235} \\ b \\gt -2 \\ ) \\ .\r\n\\end{align}\\]\r\n[4] \u3088\u308a\r\n\\[\r\n\\dfrac{1}{3} \\lt b \\lt 6 \\ .\r\n\\]\r\n[5] \u3088\u308a\r\n\\[\r\nb \\leqq 1 -\\dfrac{\\sqrt{2}}{2} , \\ 1 +\\dfrac{\\sqrt{2}}{2} \\leqq b \\ .\r\n\\]\r\n[6] \u3088\u308a\r\n\\[\r\nb \\leqq \\dfrac{9}{4} \\ .\r\n\\]\r\n[7] \u3092\u307f\u305f\u3059 \\(b\\) \u306f\u5b58\u5728\u3057\u306a\u3044.
      \r\n\u4ee5\u4e0a\u304b\u3089\r\n\\[\r\n1 +\\dfrac{\\sqrt{2}}{2} \\leqq b \\leqq \\dfrac{9}{4} \\ .\r\n\\]<\/li>\r\n<\/ol>\r\n

      1*<\/strong> , 2*<\/strong> \u3088\u308a, \u6c42\u3081\u308b \\(b\\) \u306e\u6761\u4ef6\u306f\r\n\\[\r\n\\underline{1 -\\dfrac{\\sqrt{2}}{2} \\lt b} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u66f2\u7dda \\(y = x^2\\) \u4e0a\u306b \\(2\\) \u70b9 A \\(( -2 , 4 )\\) , B \\(( b , b^2 )\\) \u3092\u3068\u308b. \u305f\u3060\u3057 \\(b \\gt -2\\) \u3068\u3059\u308b. \u3053\u306e\u3068\u304d, \u6b21\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059 \\(b\\) … \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":[156],"tags":[143,162],"class_list":["post-1851","post","type-post","status-publish","format-standard","hentry","category-nagoya_r_2016","tag-nagoya_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1851","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=1851"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1851\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1851"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1851"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}