{"id":1992,"date":"2021-11-23T09:19:39","date_gmt":"2021-11-23T00:19:39","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1992"},"modified":"2021-11-23T09:19:39","modified_gmt":"2021-11-23T00:19:39","slug":"ngr202102","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr202102\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2021\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\\(4\\) \u3064\u306e\u5b9f\u6570\u3092 \\(\\alpha = \\log_2 3\\) , \\(\\beta = \\log _3 5\\) ,\r\n\\(\\gamma = \\log _5 2\\) , \\(\\delta = \\dfrac{3}{2}\\) \u3068\u304a\u304f. \u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(\\alpha \\beta \\gamma = 1\\) \u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\alpha , \\beta , \\gamma , \\delta\\) \u3092\u5c0f\u3055\u3044\u9806\u306b\u4e26\u3079\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(p = \\alpha +\\beta +\\gamma\\) , \\(q = \\dfrac{1}{\\alpha} +\\dfrac{1}{\\beta} +\\dfrac{1}{\\gamma}\\) \u3068\u3057,\r\n\\(f(x) = x^3 +p x^2 +q x +1\\) \u3068\u3059\u308b.\r\n\u3053\u306e\u3068\u304d \\(f \\left( -\\dfrac{1}{2} \\right)\\) , \\(f( -1 )\\) \u304a\u3088\u3073 \\(f \\left( -\\dfrac{3}{2} \\right)\\) \u306e\u6b63\u8ca0\u3092\u5224\u5b9a\u305b\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\[\r\n\\alpha \\beta \\gamma = \\dfrac{\\log 3}{\\log 2} \\cdot \\dfrac{\\log 5}{\\log 3} \\cdot \\dfrac{\\log 2}{\\log 5} = 1\r\n\\]\r\n

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

    \\[\\begin{align}\r\n\\alpha -\\delta & = \\dfrac{\\log 3}{\\log 2} -\\dfrac{3}{2} = \\dfrac{\\log 9 -\\log 8}{2 \\log 2} \\gt 0 \\ , \\\\\r\n\\beta -\\delta & = \\dfrac{\\log 5}{\\log 3} -\\dfrac{3}{2} = \\dfrac{\\log 25 -\\log 27}{2 \\log 2} \\lt 0 \\ , \\\\\r\n\\beta & = \\dfrac{\\log 5}{\\log 3} \\gt 1 \\ , \\quad \\gamma = \\dfrac{\\log 2}{\\log 5} \\lt 1\r\n\\end{align}\\]\r\n\u4ee5\u4e0a\u3088\u308a\r\n\\[\r\n\\underline{\\gamma \\lt \\beta \\lt \\delta \\lt \\alpha}\r\n\\]\r\n

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

    (1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\nf(x) & = x^3 +( \\alpha +\\beta +\\gamma ) x^2 +( \\alpha \\beta +\\beta \\gamma +\\gamma \\alpha ) x +\\alpha \\beta \\gamma \\\\\r\n& = ( x +\\alpha ) ( x +\\beta ) ( x +\\gamma )\r\n\\end{align}\\]\r\n\u307e\u305f\r\n\\[\r\n\\gamma -\\dfrac{1}{2}= \\dfrac{\\log 4 -\\log 5}{2\\log 5} \\lt 0\r\n\\]\r\n(1)<\/strong> \u306e\u7d50\u679c\u3068\u3042\u308f\u305b\u3066\r\n\\[\r\n0 \\lt \\gamma \\lt \\dfrac{1}{2} \\ , \\ 1 \\lt \\beta \\lt \\dfrac{3}{2} \\lt \\alpha\r\n\\]\r\n\u3086\u3048\u306b\r\n\\[\r\n-\\alpha \\lt -\\dfrac{3}{2} \\lt -\\beta \\lt -1 \\ , \\ -\\dfrac{1}{2} \\lt -\\gamma \\lt 0\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(y = f(x)\\) \u306e\u30b0\u30e9\u30d5\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n\"ngr20210201\"\r\n

    \u3088\u3063\u3066\r\n\\[\r\n\\underline{f \\left( -\\dfrac{1}{2} \\right) \\lt 0 \\ , \\ f( -1 ) \\lt 0 \\ , \\ f \\left( -\\dfrac{3}{2} \\right) \\gt 0}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(4\\) \u3064\u306e\u5b9f\u6570\u3092 \\(\\alpha = \\log_2 3\\) , \\(\\beta = \\log _3 5\\) , \\(\\gamma = \\log _5 2\\) , \\(\\delta = \\dfrac{3}{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":[176],"tags":[143,165],"class_list":["post-1992","post","type-post","status-publish","format-standard","hentry","category-nagoya_r_2021","tag-nagoya_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1992","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=1992"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1992\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1992"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1992"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1992"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}