{"id":1013,"date":"2015-04-04T23:47:26","date_gmt":"2015-04-04T14:47:26","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1013"},"modified":"2021-03-18T09:40:36","modified_gmt":"2021-03-18T00:40:36","slug":"tkr201406","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr201406\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2014\uff1a\u7b2c6\u554f"},"content":{"rendered":"
\n

\u5ea7\u6a19\u5e73\u9762\u306e\u539f\u70b9\u3092 O \u3067\u8868\u3059. \r\n\u7dda\u5206 \\(y = \\sqrt{3} x \\quad ( 0 \\leqq x \\leqq 2 )\\) \u4e0a\u306e\u70b9 P \u3068, \u7dda\u5206 \\(y = - \\sqrt{3} x \\quad ( -2 \\leqq x \\leqq 0 )\\) \u4e0a\u306e\u70b9 Q \u304c, \u7dda\u5206 OP \u3068\u7dda\u5206 OQ \u306e\u9577\u3055\u306e\u548c\u304c \\(6\\) \u3068\u306a\u308b\u3088\u3046\u306b\u52d5\u304f. \r\n\u3053\u306e\u3068\u304d, \u7dda\u5206 PQ \u306e\u901a\u904e\u3059\u308b\u9818\u57df\u3092 \\(D\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(s\\) \u3092 \\(0 \\leqq s \\leqq 2\\) \u3092\u307f\u305f\u3059\u5b9f\u6570\u3068\u3059\u308b\u3068\u304d, \u70b9 \\((s,t)\\) \u304c \\(D\\) \u306b\u5165\u308b\u3088\u3046\u306a \\(t\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(D\\) \u3092\u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

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

    \u70b9 P , Q \u306e \\(x\\) \u5ea7\u6a19\u3092\u305d\u308c\u305e\u308c \\(p , q \\quad ( 0 \\leqq p \\leqq 2 , \\ -2 \\leqq q \\leqq 0 \\quad ... [1] )\\) \u3068\u304a\u304f.
    \r\n\\(\\text{OP} = 2p\\) , \\(\\text{OQ} = -2q\\) \u306a\u306e\u3067 \\(p , q\\) \u304c\u307f\u305f\u3059\u6761\u4ef6\u306f\r\n\\[\\begin{align}\r\n2p -2q & = 6 \\\\\r\n\\text{\u2234} \\quad q & = p-3\r\n\\end{align}\\]\r\n[1] \u3088\u308a\r\n\\[\\begin{align}\r\n0 & \\leqq p \\leqq 2 , \\quad -2 \\leqq p-3 \\leqq 0 \\\\\r\n\\text{\u2234} \\quad & 1 \\leqq p \\leqq 2 \\quad ... [2]\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u7dda\u5206 PQ \u306e\u5f0f\u306f\r\n\\[\\begin{align}\r\ny & = \\dfrac{\\sqrt{3} p +\\sqrt{3} (p-3)}{3} ( x-p ) +\\sqrt{3} p \\\\\r\n& = \\dfrac{2p-3}{\\sqrt{3}} (x-p) +\\sqrt{3} p \\quad \\left( p-3 \\leqq x \\leqq p \\right)\r\n\\end{align}\\]\r\n\u3053\u308c\u304c, \u70b9 \\(( s , t )\\) \u3092\u901a\u308a\u3068\u3059\u308c\u3070\r\n\\[\\begin{align}\r\n\\sqrt{3} t = ( 2p-3 ) ( s-p ) & +3p \\\\\r\n\\text{\u2234} \\quad 2p^2 -2 (s+3) p +3s +\\sqrt{3} t & = 0 \\quad ... [3]\r\n\\end{align}\\]\r\n\u6c42\u3081\u308b \\(s , t\\) \u306e\u6761\u4ef6\u306f, \\(p\\) \u306e \\(2\\) \u6b21\u65b9\u7a0b\u5f0f [3] \u304c, \u7bc4\u56f2 [2] \u3064\u307e\u308a \\(1 \\leqq p \\leqq 2\\) \u306b\u89e3\u3092\u3082\u3064\u6761\u4ef6\u3067\u3042\u308b.
    \r\n[3] \u306e\u5de6\u8fba\u3092 \\(f(p)\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nf(1) & = s +\\sqrt{3} t -4 \\\\\r\nf(2) & = -s +\\sqrt{3} t -4\r\n\\end{align}\\]\r\n\\(0 \\leqq s \\leqq 2\\) ... [4] \u306a\u306e\u3067, \\(f(1) \\geqq f(2)\\) .
    \r\n\\(y = f(p)\\) \u306e\u30b0\u30e9\u30d5\u306f, \u4e0b\u306b\u51f8\u3067, \\(p = \\dfrac{s+3}{2}\\) \u3092\u8ef8\u306b\u3082\u3064\u653e\u7269\u7dda\u3067\u3042\u308b.
    \r\n\u3057\u305f\u304c\u3063\u3066, \u6c42\u3081\u308b\u6761\u4ef6\u306f, [3] \u306e\u5224\u5225\u5f0f\u3092 \\(D\\) \u3068\u304a\u3051\u3070, \u4ee5\u4e0b\u306e 1*<\/strong> \u307e\u305f\u306f 2*<\/strong> \u3067\u3042\u308b.<\/p>\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(f(1) f(2) \\leqq 0\\)<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000\\(f(2) \\geqq 0\\) , \\(1 \\leqq \\dfrac{s+3}{2} \\leqq 2\\) , \\(D \\geqq 0\\)<\/p><\/li>\r\n<\/ol>\r\n

      \u305d\u308c\u305e\u308c\u3068\u304f\u3068<\/p>\r\n

        \r\n

      1. 1*<\/strong> \u306b\u3064\u3044\u3066
        \r\n\\[\\begin{align}\r\n\\left( s +\\sqrt{3} t -4 \\right) & \\left( -s +\\sqrt{3} t -4 \\right) \\leqq 0 \\\\\r\n\\text{\u2234} \\quad \\left( t +\\dfrac{\\sqrt{3} s}{3} -\\dfrac{4 \\sqrt{3}}{3} \\right) & \\left( t -\\dfrac{\\sqrt{3} s}{3} -\\dfrac{4 \\sqrt{3}}{3} \\right) \\leqq 0\r\n\\end{align}\\]<\/li>\r\n

      2. 2*<\/strong> \u306b\u3064\u3044\u3066
        \r\n\\(f(2) \\geqq 0\\) \u3088\u308a\r\n\\[\r\nt \\geqq \\dfrac{\\sqrt{3} s}{3} +\\dfrac{4 \\sqrt{3}}{3}\r\n\\]\r\n\\(1 \\leqq \\dfrac{s+3}{2} \\leqq 2\\) \u3088\u308a\r\n\\[\r\n-1 \\leqq s \\leqq 1\r\n\\]\r\n\u305f\u3060\u3057, [4] \u306a\u306e\u3067\r\n\\[\r\n0 \\leqq s \\leqq 1\r\n\\]\r\n\\(D \\geqq 0\\) \u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{D}{4} & = (s+3)^2 -2 \\left( 3s +\\sqrt{3} t \\right) \\geqq 0 \\\\\r\n& s^2 +9 -2 \\sqrt{3} t \\geqq 0 \\\\\r\n\\text{\u2234} \\quad & t \\geqq \\dfrac{\\sqrt{3} s^2}{6} +\\dfrac{3 \\sqrt{3}}{2}\r\n\\end{align}\\]\r\n\u3053\u308c\u3089\u306e\u6761\u4ef6\u306b\u52a0\u3048\u3066, \u7dda\u5206 PQ \u306f, \u9818\u57df\uff1a \\(y \\geqq \\sqrt{3} x\\) \u306b\u3042\u308b\u306e\u3067, \u6c42\u3081\u308b\u7bc4\u56f2\u306f\u4e0b\u56f3\u306e\u659c\u7dda\u90e8\uff08\u5883\u754c\u542b\u3080\uff09\u3068\u306a\u308b.<\/p><\/li>\r\n<\/ol>\r\n\"tokyor20140601\"\r\n

        \u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u6761\u4ef6\u306f\r\n\\[\r\n\\underline{\\left\\{ \\begin{array}{ll} - \\dfrac{\\sqrt{3} s}{3} +\\dfrac{4 \\sqrt{3}}{3} \\leqq t \\leqq \\dfrac{\\sqrt{3} s^2}{6} +\\dfrac{3 \\sqrt{3}}{2} & \\left( 0 \\leqq s \\lt 1 \\text{\u306e\u3068\u304d} \\right) \\\\ \\sqrt{3} s \\leqq t \\leqq \\dfrac{\\sqrt{3} s}{3} +\\dfrac{4 \\sqrt{3}}{3} & \\left( 1 \\leqq s \\leqq 2 \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right.}\r\n\\]\r\n

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

        (1)<\/strong> \u306e\u7d50\u679c\u306f, \\(0 \\leqq x \\leqq 2\\) \u306b\u304a\u3051\u308b\u7dda\u5206 PQ \u306e\u901a\u904e\u9818\u57df\u3067\u3042\u308b.
        \r\n\u6c42\u3081\u308b\u9818\u57df \\(D\\) \u306f, \\(y\\) \u8ef8\u306b\u3064\u3044\u3066\u5bfe\u79f0\u306a\u306e\u3067, \\(D\\) \u306f\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u542b\u3080\uff09\u3068\u306a\u308b.<\/p>\r\n\"tokyor20140602\"\r\n","protected":false},"excerpt":{"rendered":"\u5ea7\u6a19\u5e73\u9762\u306e\u539f\u70b9\u3092 O \u3067\u8868\u3059. \u7dda\u5206 \\(y = \\sqrt{3} x \\quad ( 0 \\leqq x \\leqq 2 )\\) \u4e0a\u306e\u70b9 P \u3068, \u7dda\u5206 \\(y = - \\sqrt{3} x \\quad ( -2 \\l … \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":[113],"tags":[139,112],"class_list":["post-1013","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2014","tag-tokyo_r","tag-112"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1013","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=1013"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1013\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1013"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1013"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1013"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}