\r\n \r\n
\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n
(1)<\/strong><\/p>\r\n\\(a = b\\) \u306e\u3068\u304d\r\n\\[\r\nx^2+ax+a = 0\n\\]\r\n\u3053\u306e\u65b9\u7a0b\u5f0f\u306e \\(2\\) \u3064\u306e\u6574\u6570\u89e3 \\(\\alpha , \\beta\\) \u3068\u304a\u304f\u3068, \u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3088\u308a\r\n\\[\r\n\\alpha +\\beta =-a , \\ \\alpha \\beta =a \\quad ... [1]\n\\]\r\n\u307e\u305f, \\(a \\gt 0\\) \u306a\u306e\u3067, \\(\\alpha \\leqq \\beta \\leqq -1 \\quad ... [2]\\) \u3068\u304a\u3044\u3066\u3088\u3044.
\r\n[1] \u304b\u3089 \\(a\\) \u3092\u6d88\u53bb\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n\\alpha +\\beta +\\alpha \\beta & = 0 \\\\\r\n( \\alpha +1 )( \\beta +1 ) & = 1 \\\\\r\n\\text{\u2234} \\quad ( \\alpha , \\beta ) & = ( -2 , -2 ) \\quad ( \\ \\text{\u2235} \\ [2] \\ )\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\na = (-2)(-2) = \\underline{4}\n\\]\r\n
(2)<\/strong><\/p>\r\n\\(x^2+ax+b = 0\\) \u306e \\(2\\) \u3064\u306e\u6574\u6570\u89e3\u3092 \\(\\alpha , \\beta\\) , \\(y^2+by+a = 0\\) \u306e \\(2\\) \u3064\u306e\u6574\u6570\u89e3\u3092 \\(\\gamma , \\delta\\) \u3068\u304a\u304f.
\r\n\u89e3\u3068\u4fc2\u6570\u306e\u95a2\u4fc2\u3088\u308a\r\n\\[\r\n\\left\\{ \\begin{array}{ll} \\alpha +\\beta =-a , & \\alpha \\beta =b \\\\ \\gamma +\\delta =-b , & \\gamma \\delta =a \\end{array} \\right. \\quad ... [3]\n\\]\r\n\u307e\u305f, \\(a \\gt b \\gt 0\\) \u306a\u306e\u3067, \\(\\alpha \\leqq \\beta \\leqq -1 , \\ \\gamma \\leqq \\delta \\leqq -1\\) ...[4] \u3068\u3057\u3066\u3088\u3044.
\r\n[3] \u304b\u3089 \\(a , b\\) \u3092\u6d88\u53bb\u3059\u308b\u3068\r\n\\[\r\n\\left\\{ \\begin{array}{l} \\alpha +\\beta +\\gamma \\delta =0 \\\\ \\gamma +\\delta +\\alpha \\beta=0 \\end{array} \\right.\n\\]\r\n\u3055\u3089\u306b\u8fba\u3005\u3092\u52a0\u3048\u308b\u3068\r\n\\[\\begin{align}\r\n\\alpha \\beta +\\alpha +\\beta +\\gamma \\delta +\\gamma +\\delta & = 0 \\\\\r\n\\text{\u2234} \\quad ( \\alpha +1 )( \\beta +1 ) +( \\gamma +1 )( \\delta +1 ) & = 2 \\quad ... [5]\n\\end{align}\\]\r\n\u8fba\u3005\u3092\u5dee\u5f15\u304f\u3068\r\n\\[\\begin{align}\r\n\\alpha \\beta -\\alpha -\\beta -\\gamma \\delta +\\gamma +\\delta & = 0 \\\\\r\n\\text{\u2234} \\quad ( \\alpha -1 )( \\beta -1 ) = ( \\gamma -1 )( \\delta -1 ) & \\quad ... [6]\n\\end{align}\\]\r\n[5] \u306b\u3064\u3044\u3066, [3] [4] \u3088\u308a,\r\n\\[\r\n( \\alpha +1 )( \\beta +1 ) =a-b+1 \\geqq 2 , \\ ( \\gamma +1 )( \\delta +1 ) \\geqq 0\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n& \\left\\{ \\begin{array}{l} ( \\alpha +1 )( \\beta +1 ) =2 \\\\ ( \\gamma +1 )( \\delta +1 )=0 \\end{array} \\right. \\\\\r\n\\text{\u2234} & \\quad \\alpha = -3 , \\ \\beta = -2 , \\ \\delta = -1 \\quad ( \\ \\text{\u2235} \\ [4] \\ )\n\\end{align}\\]\r\n[6] \u306b\u4ee3\u5165\u3059\u308c\u3070\r\n\\[\\begin{align}\r\n(-4)(-3) & = ( \\gamma -1)(-2) \\\\\r\n\\text{\u2234} \\quad \\gamma & = -5\n\\end{align}\\]\r\n\u4ee5\u4e0a\u3088\u308a\r\n\\[\r\n( a , b ) = \\left( (-3)(-2) , (-5)(-1) \\right) = \\underline{( 6 , 5 )}\n\\]\r\n\r\n
\r\n « \u89e3\u7b54\u3092\u96a0\u3059 <\/a>\r\n <\/p>\r\n <\/div>","protected":false},"excerpt":{"rendered":"\\(a , b\\) \u306f \\(a \\geqq b \\gt 0\\) \u3092\u6e80\u305f\u3059\u6574\u6570\u3068\u3057, \\(x\\) \u3068 \\(y\\) \u306e \\(2\\) \u6b21\u65b9\u7a0b\u5f0f \\(x^2+ax+b = 0\\) , \\(y^2+by+a = 0\\) \u304c\u305d\u308c\u305e\u308c […]","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":[35],"tags":[143,13],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/57"}],"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=57"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/57\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=57"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=57"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=57"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}