{"id":722,"date":"2013-04-10T00:13:04","date_gmt":"2013-04-09T15:13:04","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=722"},"modified":"2021-11-04T16:06:32","modified_gmt":"2021-11-04T07:06:32","slug":"htb200703","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb200703\/","title":{"rendered":"\u4e00\u6a4b\u59272007\uff1a\u7b2c3\u554f"},"content":{"rendered":"
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\u653e\u7269\u7dda \\(y=ax^2+bx \\ ( a \\gt 0 )\\) \u3092 \\(C\\) \u3068\u3059\u308b.\r\n\\(C\\) \u4e0a\u306b\u7570\u306a\u308b \\(2\\) \u70b9 P , Q \u3092\u3068\u308a, \u305d\u306e \\(x\\) \u5ea7\u6a19\u3092\u305d\u308c\u305e\u308c \\(p , q \\ ( 0 \\lt p \\lt q )\\) \u3068\u3059\u308b.<\/p>\r\n

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  1. (1)<\/strong>\u3000\u7dda\u5206 OQ \u3068 \\(C\\) \u3067\u56f2\u307e\u308c\u305f\u90e8\u5206\u306e\u9762\u7a4d\u304c, \u25b3OPQ \u306e\u9762\u7a4d\u306e \\(\\dfrac{3}{2}\\) \u500d\u3067\u3042\u308b\u3068\u304d, \\(p\\) \u3068 \\(q\\) \u306e\u95a2\u4fc2\u3092\u6c42\u3081\u3088. \u305f\u3060\u3057, O \u306f\u539f\u70b9\u3092\u8868\u3059.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000Q \u3092\u56fa\u5b9a\u3057\u3066 P \u3092\u52d5\u304b\u3059. \u25b3OPQ \u306e\u9762\u7a4d\u304c\u6700\u5927\u3068\u306a\u308b\u3068\u304d\u306e \\(p\\) \u3092 \\(q\\) \u3067\u8868\u305b. \u307e\u305f, \u305d\u306e\u3068\u304d\u306e \u25b3OPQ \u306e\u9762\u7a4d\u3068, \u7dda\u5206 OQ \u3068 \\(C\\) \u3067\u56f2\u307e\u308c\u305f\u90e8\u5206\u306e\u9762\u7a4d\u3068\u306e\u6bd4\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \u7dda\u5206 OQ \u3068 \\(C\\) \u306b\u56f2\u307e\u308c\u305f\u90e8\u5206, \u25b3OPQ \u306e\u9762\u7a4d\u3092\u305d\u308c\u305e\u308c \\(S , T\\) \u3068\u304a\u304f.\r\n\\[\\begin{align}\r\nS & = -\\displaystyle\\int _ 0^q ax(x-q) \\, dx \\\\\r\n& = \\dfrac{1}{6} aq^3 , \\\\\r\nT & = \\dfrac{1}{2} \\left| p (aq^2+bq) -q (ap^2+bp) \\right| \\\\\r\n& = \\dfrac{1}{2} apq(q-p)\r\n\\end{align}\\]\r\n\\(S = \\dfrac{3}{2} T\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\dfrac{1}{6} aq^3 & = \\dfrac{3}{2} \\cdot \\dfrac{1}{2} apq(q-p) \\\\\r\n2q^2 -9pq +9p^2 & = 0 \\\\\r\n(2q-3p)(q-3p) & = 0\r\n\\text{\u2234} \\quad \\underline{ q = 3p , \\dfrac{3p}{2}} &\r\n\\end{align}\\]\r\n

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

    \\[\r\nT = \\dfrac{aq}{2} \\left\\{ -\\left( p -\\dfrac{q}{2} \\right)^2 +\\dfrac{q^2}{4} \\right\\}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(T\\) \u3092\u6700\u5927\u306b\u3059\u308b \\(p\\) \u306f\r\n\\[\r\np = \\underline{\\dfrac{q}{2}}\r\n\\]\r\n\u3053\u308c\u306f, \\(0 \\lt p \\lt q\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u308b.
    \r\n\u3053\u306e\u3068\u304d\r\n\\[\\begin{align}\r\nT : S & = \\dfrac{1}{8} aq^3 : \\dfrac{1}{6} aq^3 \\\\\r\n& = \\underline{3 : 4}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u653e\u7269\u7dda \\(y=ax^2+bx \\ ( a \\gt 0 )\\) \u3092 \\(C\\) \u3068\u3059\u308b. \\(C\\) \u4e0a\u306b\u7570\u306a\u308b \\(2\\) \u70b9 P , Q \u3092\u3068\u308a, \u305d\u306e \\(x\\) \u5ea7\u6a19\u3092\u305d\u308c\u305e\u308c \\(p , q \\ ( 0 \\lt … \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":[107],"tags":[146,109],"class_list":["post-722","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2007","tag-hitotsubashi","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/722","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=722"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/722\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=722"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=722"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=722"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}