{"id":1532,"date":"2015-12-15T13:00:09","date_gmt":"2015-12-15T04:00:09","guid":{"rendered":"http:\/\/math.co.jp\/blog\/?p=1532"},"modified":"2015-12-15T18:25:01","modified_gmt":"2015-12-15T09:25:01","slug":"%e5%88%86%e6%95%b0%e4%b8%8d%e7%ad%89%e5%bc%8f-%e8%a7%a3%e7%ad%94%e7%b7%a8","status":"publish","type":"post","link":"https:\/\/math.co.jp\/blog\/?p=1532","title":{"rendered":"\u5206\u6570\u4e0d\u7b49\u5f0f (\u89e3\u7b54\u7de8)"},"content":{"rendered":"

(1)\u3000\u307e\u305a, \u4e0e\u3048\u3089\u308c\u305f\u5f0f\u306f\u4e0d\u7b49\u5f0f\u3067\u3059\u306e\u3067,
\n\u300c\\(\\displaystyle\\frac{2x-1}{x+2}>x-1\\) \u306e\u5206\u6bcd\u3092\u306f\u3089\u3063\u3066<\/p>\n

\u3000\u3000\u3000\u3000\\(2x-1\\gt (x-1)(x+2)\\)\u300d\u3000\u3000(\\(\\leftarrow\\) \u8aa4\u308a!<\/strong>)<\/p>\n

\u306e\u3088\u3046\u306b\u306f\u306a\u3089\u306a\u3044<\/strong>\u3053\u3068\u306b\u6ce8\u610f\u3057\u307e\u3057\u3087\u3046\u3002\u306a\u305c\u306a\u3089\u3070, \\((x+2)\\) \u306f\u6b63\u3067\u3042\u308b\u3068\u306f\u9650\u3089\u306a\u3044\u304b\u3089\u3067\u3059\u3002\\(x+2\\gt 0\\) \u3067\u3042\u308b\u3088\u3046\u306a\u5834\u5408, \u3064\u307e\u308a \\(x\\gt -2\\) \u3067\u3042\u308b\u5834\u5408\u306f, \u4e0e\u3048\u3089\u308c\u305f\u4e0d\u7b49\u5f0f\u306f,
\n\u3000\u3000\u3000\u3000\\(2x-1\\gt (x-1)(x+2)\\)
\n\u3068\u306a\u308a\u307e\u3059\u304c, \\(x+2\\lt 0\\) \u3064\u307e\u308a \\(x\\lt -2\\) \u3067\u3042\u308b\u5834\u5408\u306f, \u4e0e\u3048\u3089\u308c\u305f\u4e0d\u7b49\u5f0f\u306f,
\n\u3000\u3000\u3000\u3000\\(2x-1\\lt (x-1)(x+2)\\)
\n\u3068\u306a\u308a\u307e\u3059\u3002\u3067\u3059\u304b\u3089, \\(x\\gt -2\\) \u306e\u5834\u5408\u3068 \\(x\\lt -2\\) \u306e\u5834\u5408\u306b\u5206\u3051\u3066\u4e0d\u7b49\u5f0f\u3092\u89e3\u3051\u3070\u6b63\u89e3\u304c\u5f97\u3089\u308c\u307e\u3059\u3002
\n\u3082\u3061\u308d\u3093\u3053\u306e\u65b9\u6cd5\u3067\u3082\u3088\u3044\u306e\u3067\u3059\u304c, \u3053\u3053\u3067\u306f\u5834\u5408\u5206\u3051\u3092\u3057\u306a\u3044\u65b9\u6cd5\u3067\u89e3\u3044\u3066\u307f\u307e\u3059\u3002\u305d\u308c\u306f\u4e21\u8fba\u306b \\((\u5206\u6bcd)^{2}\\), \u3059\u306a\u308f\u3061, \\((x+2)^{2}\\) \u3092\u66f8\u3051\u308b\u65b9\u6cd5\u3067\u3059\u3002\\(x+2\\neq 0\\) \u306e\u3068\u304d\u306f \\((x+2)^{2}\\gt 0\\) \u3067\u3059\u306e\u3067, \u6b21\u306e\u3088\u3046\u306a\u65b9\u6cd5\u304c\u53ef\u80fd\u3067\u3059\u3002\u305f\u3060\u3057, 3 \u6b21\u4e0d\u7b49\u5f0f\u3092\u89e3\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n

\u4e0e\u3048\u3089\u308c\u305f\u4e0d\u7b49\u5f0f \\(\\displaystyle\\frac{2x-1}{x+2}\\gt x-1\\) \u306e\u4e21\u8fba\u306b \\((x+2)^{2}\\) \u3092\u304b\u3051\u3066
\n\u3000\u3000\u3000\u3000\\((2x-1)(x+2)\\gt (x-1)(x+2)^{2}\\)
\n\u3000\u3000\u3000\u3000\\((x-1)(x+2)^{2}-(2x-1)(x+2)\\lt 0\\)
\n\u3000\u3000\u3000\u3000\\((x+2)\\{(x-1)(x+2)-(2x-1)\\}\\lt 0\\)
\n\u3000\u3000\u3000\u3000\\((x+2)(x^{2}-x-1)\\lt 0\\)
\n\u3000\u3000\u3000\u3000\\((x+2)\\left( x-\\displaystyle\\frac{1+\\sqrt{5}}{2}\\right)\\left( x-\\displaystyle\\frac{1-\\sqrt{5}}{2}\\right)\\lt 0\\)
\n\u3068\u306a\u308b\u3002\u3053\u3053\u3067, \\(-2\\lt \\displaystyle\\frac{1-\\sqrt{5}}{2}\\lt \\displaystyle\\frac{1+\\sqrt{5}}{2}\\)
\n\u3067\u3042\u308b\u304b\u3089, \u4e0d\u7b49\u5f0f\u306e\u89e3\u306f,
\n\u3000\u3000\u3000\u3000\\(x\\lt -2\\), \\(\\displaystyle\\frac{1-\\sqrt{5}}{2}\\lt x\\lt \\displaystyle\\frac{1+\\sqrt{5}}{2}\\)\u3000\u3000(\u7b54)<\/div>\n

(2) \u4e21\u8fba\u306b \\((x+2)^{2}\\) \u3092\u304b\u3051\u308b\u65b9\u6cd5\u3067 (1) \u3092\u6c42\u3081\u307e\u3057\u305f\u304c, \u540c\u3058\u3088\u3046\u306b\u8003\u3048\u3066,<\/p>\n

\u3000\\(\\displaystyle\\frac{2x-1}{x+2}\\geqq x-1\\iff (2x-1)(x+2)\\geqq (x-1)(x+2)^{2}\\)<\/p>\n

\u306e\u3088\u3046\u306b\u306a\u308b\u304b\u3068\u3044\u3046\u3068, \u4eca\u5ea6\u306f\u6b63\u3057\u304f\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3069\u3053\u304c\u6b63\u3057\u304f\u306a\u3044\u304b\u3068\u3044\u3046\u3068, \u305d\u308c\u306f, \u5de6\u8fba\u306f \\(x=-2\\) \u3067\u306f\u6210\u308a\u7acb\u305f\u306a\u3044\u306e\u306b\u53f3\u8fba\u3067\u306f \\(x=-2\\) \u3067\u6210\u308a\u7acb\u3063\u3066\u3057\u307e\u3046\u70b9\u3067\u3059\u3002\u3064\u307e\u308a,<\/p>\n

\u3000\u3000\u3000\u300c(1) \u3067\u6c42\u3081\u305f\u89e3\u306b\u7b49\u53f7\u3092\u5165\u308c\u308c\u3070\u3088\u3044\u300d\u3068\u3044\u3046\u8003\u3048\u306f\u8aa4\u308a<\/strong><\/p>\n

\u306a\u306e\u3067\u3059\u3002\u4e00\u822c\u306b, \u5206\u6bcd\u3092\u6255\u3046\u3068\u304d\u306f, \u6255\u3063\u305f\u5f8c\u3067\u300c\u5143\u5206\u6bcd\u304c 0 \u3067\u306a\u3044\u300d\u3053\u3068\u306b\u6ce8\u610f\u3057\u307e\u3059\u3002\u3064\u307e\u308a,<\/p>\n

\u3000\u3000\\(\\displaystyle\\frac{a}{b}=c\\iff a=bc\\) \u306f\u8aa4\u308a!<\/strong>
\n\u3067\u3042\u3063\u3066,
\n\u3000\u3000\\(\\displaystyle\\frac{a}{b}=c\\iff a=bc\\ \u304b\u3064\\ b\\neq 0\\)
\n\u306a\u306e\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066, \u3053\u3053\u3067\u306f,<\/p>\n

\u3000\u3000\\(\\displaystyle\\frac{2x-1}{x+2}\\geqq x-1\\iff (2x-1)(x+2)\\geqq (x-1)(x+2)^{2}\\) \u304b\u3064 \\(x+2\\neq 0\\)<\/p>\n

\u3068\u3057\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002
\n\u306a\u304a, (1) \u3067
\n\u3000\u3000\\(\\displaystyle\\frac{2x-1}{x+2}\\gt x-1\\iff (2x-1)(x+2)\\gt (x-1)(x+2)^{2}\\)
\n\u306e\u3088\u3046\u306b \\(x+2\\neq 0\\) \u3092\u66f8\u304b\u306a\u304f\u3066\u3082\u3088\u304b\u3063\u305f\u306e\u306f, \u53f3\u5074\u306e\u6761\u4ef6\u304c \\(x+2\\neq 0\\) \u3092\u542b\u3093\u3067\u3044\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n

\u4e0e\u3048\u3089\u308c\u305f\u4e0d\u7b49\u5f0f \\(\\displaystyle\\frac{2x-1}{x+2}\\geqq x-1\\) \u306e\u4e21\u8fba\u306b \\((x+2)^{2}\\) \u3092\u304b\u3051\u3066
\n\u3000\u3000\\((2x-1)(x+2)\\geqq (x-1)(x+2)^{2}\\ \\ \\cdots\\cdots\\,\u2460\\) \u304b\u3064 \\(x+2\\neq 0\\ \\ \\cdots\\cdots\\,\u2461\\)
\n\u3053\u3053\u3067, \u2460\u306f (1) \u3092\u5229\u7528\u3059\u308b\u3068,
\n\u3000\u3000\\(x\\leqq -2\\), \\(\\displaystyle\\frac{1-\\sqrt{5}}{2}\\leqq x\\leqq \\displaystyle\\frac{1+\\sqrt{5}}{2}\\)
\n\u3053\u308c\u3068 \u2461 \u3088\u308a \\(x\\neq -2\\) \u3092\u3068\u3082\u306b\u6e80\u305f\u3059\u7bc4\u56f2\u3092\u6c42\u3081\u3066,
\n\u3000\u3000\\(x\\lt -2\\), \\(\\displaystyle\\frac{1-\\sqrt{5}}{2}\\leqq x\\leqq \\displaystyle\\frac{1+\\sqrt{5}}{2}\\)\u3000\u3000(\u7b54)<\/div>\n","protected":false},"excerpt":{"rendered":"

(1)\u3000\u307e\u305a, \u4e0e\u3048\u3089\u308c\u305f\u5f0f\u306f\u4e0d\u7b49\u5f0f\u3067\u3059\u306e\u3067, \u300c\\(\\displaystyle\\frac{2x-1}{x+2}>x-1\\) \u306e\u5206\u6bcd\u3092\u306f\u3089\u3063\u3066 \u3000\u3000\u3000\u3000\\(2x-1\\gt (x-1)(x+2)\\)\u300d\u3000\u3000(\\(\\le […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[21],"class_list":["post-1532","post","type-post","status-publish","format-standard","hentry","category-11","tag-etude-knowledge"],"_links":{"self":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1532","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1532"}],"version-history":[{"count":5,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1532\/revisions"}],"predecessor-version":[{"id":1538,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1532\/revisions\/1538"}],"wp:attachment":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1532"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1532"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1532"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}