{"id":330,"date":"2012-03-04T22:30:59","date_gmt":"2012-03-04T13:30:59","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=330"},"modified":"2021-10-03T20:45:43","modified_gmt":"2021-10-03T11:45:43","slug":"kbr200801","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kbr200801\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2008\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\\(p , q\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b. \\(x\\) \u306e\u65b9\u7a0b\u5f0f\r\n\\[\r\n\\log _ {10} (px) \\cdot \\log _ {10} (qx) +1 = 0\r\n\\]\r\n\u304c \\(1\\) \u3088\u308a\u5927\u304d\u3044\u89e3\u3092\u3082\u3064\u3068\u304d, \u70b9 \\(\\left( \\log _ {10} p , \\log _ {10} q \\right)\\) \u306e\u5b58\u5728\u3059\u308b\u7bc4\u56f2\u3092\u5ea7\u6a19\u5e73\u9762\u4e0a\u306b\u56f3\u793a\u305b\u3088.<\/p>\r\n

\r\n\r\n

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

\\(P =\\log _ {10} p\\) , \\(Q =\\log _ {10} q\\) , \\(X =\\log _ {10} x\\) \u3068\u304a\u304f\u3068, \u4e0e\u3048\u3089\u308c\u305f\u65b9\u7a0b\u5f0f\u306f\r\n\\[\\begin{align}\r\n(X+P)(X+Q) +1 & = 0 \\\\\r\n\\text{\u2234} \\quad X^2 +(P+Q)X +PQ+1 & = 0 \\quad ... [1]\r\n\\end{align}\\]\r\n\\(x \\gt 1\\) \u306e\u3068\u304d, \\(X \\gt 0\\) \u306a\u306e\u3067, \\(X\\) \u306b\u3064\u3044\u3066\u306e\u65b9\u7a0b\u5f0f [1] \u304c\u6b63\u306e\u89e3\u3092\u3082\u3064\u305f\u3081\u306e \\(P , Q\\) \u306e\u6761\u4ef6\u3092\u6c42\u3081\u308c\u3070\u3088\u3044.
\r\n[1] \u306e\u5de6\u8fba\u3092 \\(f(X)\\) \u3068\u304a\u304d, \u5224\u5225\u5f0f\u3092 \\(D\\) \u3068\u3059\u308c\u3070\r\n\\[\\begin{align}\r\nf(X) & = \\left( X +\\dfrac{P+Q}{2} \\right)^2 -\\dfrac{(P-Q)^2}{4}+1 , \\\\\r\nD & = (P+Q)^2 -4( PQ+1 ) = (P-Q)^2 -4 \\\\\r\n& = (P+Q-2)(P-Q-2)\r\n\\end{align}\\]\r\n\u3086\u3048\u306b, \u6c42\u3081\u308b\u6761\u4ef6\u306f, \u6b21\u306b\u3042\u3052\u308b 1*<\/strong> \u307e\u305f\u306f 2*<\/strong> \u306e\u3068\u304d\u3067\u3042\u308b.<\/p>\r\n

    \r\n

  1. 1*<\/strong>\u3000\\(f(X) = 0\\) \u304c, \u6b63\u306e\u89e3\u3092 \\(1\\) \u3064\u3060\u3051\u3082\u3064\u3068\u304d\r\n\\[\\begin{align}\r\nf(0) = PQ+1 & \\lt 0 \\\\\r\n\\text{\u2234} \\quad PQ & \\lt -1\r\n\\end{align}\\]<\/li>\r\n

  2. 2*<\/strong>\u3000\\(f(X) = 0\\) \u304c, \u6b63\u306e\u89e3\u3092 \\(2\\) \u3064\uff08\u91cd\u89e3\u3092\u542b\u3080\uff09\u3082\u3064\u3068\u304d\r\n\\[\\begin{align}\r\nf(0) \\geqq 0 , \\ -\\dfrac{P+Q}{2} & \\gt 0 , \\ D \\geqq 0 \\\\\r\n\\text{\u2234} \\quad PQ \\geqq -1 , \\ P+Q & \\lt 0 , \\ (P+Q-2)(P-Q-2) \\geqq 0\r\n\\end{align}\\]<\/li>\r\n<\/ol>\r\n

    \u3088\u3063\u3066, \u6c42\u3081\u308b\u9818\u57df\u306f\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u7dda\u306e\u3046\u3061, \u70b9\u7dda, \u25cb\u306f\u542b\u307e\u305a, \u5b9f\u7dda\u306f\u542b\u3080\uff09\u3068\u306a\u308b.<\/p>\r\n\"\"\r\n","protected":false},"excerpt":{"rendered":"\\(p , q\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b. \\(x\\) \u306e\u65b9\u7a0b\u5f0f \\[ \\log _ {10} (px) \\cdot \\log _ {10} (qx) +1 = 0 \\] \u304c \\(1\\) \u3088\u308a\u5927\u304d\u3044\u89e3\u3092\u3082\u3064\u3068\u304d, \u70b9 \\(\\ … \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":[55],"tags":[144,16],"class_list":["post-330","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2008","tag-tsukuba_r","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/330","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=330"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/330\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=330"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=330"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=330"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}