{"id":1378,"date":"2017-02-17T21:53:06","date_gmt":"2017-02-17T12:53:06","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1378"},"modified":"2021-09-24T21:06:52","modified_gmt":"2021-09-24T12:06:52","slug":"tkr201603","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr201603\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2016\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\\(a\\) \u3092 \\(1 \\lt a \\lt 3\\) \u3092\u307f\u305f\u3059\u5b9f\u6570\u3068\u3057,\r\n\u5ea7\u6a19\u7a7a\u9593\u5185\u306e \\(4\\) \u70b9 \\(\\text{P} {} _ 1 \\ ( 1 , 0 , 1 )\\) , \\(\\text{P} {} _ 2 \\ ( 1 , 1 , 1 )\\) , \\(\\text{P} {} _ 3 \\ ( 1 , 0 , 3 )\\) , \\(\\text{Q} \\ ( 0 , 0 , a )\\) \u3092\u8003\u3048\u308b.\r\n\u76f4\u7dda \\(\\text{P} {} _ 1 \\text{Q}\\) , \\(\\text{P} {} _ 2 \\text{Q}\\) , \\(\\text{P} {} _ 3 \\text{Q}\\) \u3068 \\(xy\\) \u5e73\u9762\u306e\u4ea4\u70b9\u3092\u305d\u308c\u305e\u308c \\(\\text{R} {} _ 1\\) , \\(\\text{R} {} _ 2\\) , \\(\\text{R} {} _ 3\\) \u3068\u3057\u3066, \u4e09\u89d2\u5f62 \\(\\text{R} {} _ 1 \\text{R} {} _ 2 \\text{R} {} _ 3\\) \u306e\u9762\u7a4d\u3092 \\(S(a)\\) \u3068\u3059\u308b.\r\n\\(S(a)\\) \u3092\u6700\u5c0f\u306b\u3059\u308b \\(a\\) \u3068, \u305d\u306e\u3068\u304d\u306e \\(S(a)\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p>\r\n

\r\n\r\n

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

\u70b9 \\(\\text{P}' {} _ 1 \\ ( 0 , 0 , 1 )\\) \u3068\u304a\u3051\u3070, \\(\\triangle \\text{QP} {} _ 1 \\text{P}' {} _ 1 \\sim \\triangle \\text{QR} {} _ 1 \\text{O}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\na : a-1 & = \\text{OR} {} _ 1 : 1 \\\\\r\n\\text{\u2234} \\quad \\text{OR} {} _ 1 & = \\dfrac{a}{a-1}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066,\u3000\\(\\text{R} {} _ 1 \\ \\left( \\dfrac{a}{a-1} , 0 , 0 \\right)\\) .
\r\n\u307e\u305f, \u70b9 \\(\\text{P}' {} _ 3 \\ ( 0 , 0 , 3 )\\) \u3068\u304a\u3051\u3070, \\(\\triangle \\text{QP} {} _ 3 \\text{P}' {} _ 3 \\sim \\triangle \\text{QR} {} _ 3 \\text{O}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\na : 3-a & = 1 : \\text{OR} {} _ 3 \\\\\r\n\\text{\u2234} \\quad \\text{OR} {} _ 3 & = \\dfrac{a}{3-a}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066,\u3000\\(\\text{R} {} _ 3 \\ \\left( \\dfrac{a}{3-a} , 0 , 0 \\right)\\) .
\r\n\u3055\u3089\u306b, \\(\\triangle \\text{QP} {} _ 1 \\text{P} {} _ 2 \\sim \\triangle \\text{QR} {} _ 1 \\text{R} {} _ 2\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\na : a-1 & = \\text{R} {} _ 1 \\text{R} {} _ 2 : 1 \\\\\r\n\\text{\u2234} \\quad \\text{R} {} _ 1 \\text{R} {} _ 2 & = \\dfrac{a}{a-1}\r\n\\end{align}\\]\r\n\\(\\text{R} {} _ 1 \\text{R} {} _ 2 \/ \\hspace{-0.2em} \/ \\text{P} {} _ 1 \\text{P} {} _ 2\\) \u306a\u306e\u3067,\u3000\\(\\text{R} {} _ 2 \\ \\left( \\dfrac{a}{a-1} , \\dfrac{a}{a-1} , 0 \\right)\\) .
\r\n\u4ee5\u4e0a\u306e\u7d50\u679c\u3088\u308a\r\n\\[\\begin{align}\r\nS(a) & = \\dfrac{1}{2} \\left( \\dfrac{a}{a-1} +\\dfrac{a}{3-a} \\right) \\cdot \\dfrac{a}{a-1} \\\\\r\n& = \\dfrac{a^2}{(a-1)^2 (3-a)}\r\n\\end{align}\\]\r\n\\(f(a) = \\dfrac{1}{S(a)}\\) \u3068\u304a\u3044\u3066, \\(f(a)\\) \u304c\u6700\u5927\u306b\u306a\u308b\u3068\u304d\u306b\u3064\u3044\u3066\u8003\u3048\u308c\u3070\u3088\u3044.\r\n\\[\\begin{align}\r\nf(a) & = \\dfrac{-a^3 +5a^2 -7a +3}{a^2} \\\\\r\n& = -a +5 -\\dfrac{7}{a} +\\dfrac{3}{a^2}\r\n\\end{align}\\]\r\n\\(a\\) \u3067\u5fae\u5206\u3059\u308b\u3068\r\n\\[\\begin{align}\r\nf'(a) & = -1 +\\dfrac{7}{a^2} -\\dfrac{6}{a^3} \\\\\r\n& = -\\dfrac{a^3 -7a +6}{a^3} \\\\\r\n& = -\\dfrac{(a-1)(a-2)(a+3)}{a^3}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(f(a)\\) \u306e\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|ccccc} a & (1) & \\cdots & 2 & \\cdots & (3) \\\\ \\hline f'(a) & & + & 0 & - & \\\\ \\hline f(a) & & \\nearrow & \\text{\u6700\u5927} & \\searrow & \\end{array}\r\n\\]\r\n\u3088\u3063\u3066, \\(S(a)\\) \u304c\u6700\u5c0f\u3068\u306a\u308b\u306e\u306f\r\n\\[\r\na = \\underline{2}\r\n\\]\r\n\u306e\u3068\u304d\u3067\r\n\\[\r\nS (2) = \\underline{4}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(a\\) \u3092 \\(1 \\lt a \\lt 3\\) \u3092\u307f\u305f\u3059\u5b9f\u6570\u3068\u3057, \u5ea7\u6a19\u7a7a\u9593\u5185\u306e \\(4\\) \u70b9 \\(\\text{P} {} _ 1 \\ ( 1 , 0 , 1 )\\) , \\(\\text{P} {} _ 2 \\ ( … \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":[150],"tags":[139,162],"class_list":["post-1378","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2016","tag-tokyo_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1378","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=1378"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1378\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1378"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1378"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1378"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}