{"id":1525,"date":"2015-12-11T18:00:07","date_gmt":"2015-12-11T09:00:07","guid":{"rendered":"http:\/\/math.co.jp\/blog\/?p=1525"},"modified":"2015-12-11T18:00:07","modified_gmt":"2015-12-11T09:00:07","slug":"%e7%b5%b6%e5%af%be%e5%80%a4%e8%a8%98%e5%8f%b7%e3%82%92%e5%90%ab%e3%82%80%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%a8%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=1525","title":{"rendered":"\u7d76\u5bfe\u5024\u8a18\u53f7\u3092\u542b\u3080\u65b9\u7a0b\u5f0f\u3068\u4e0d\u7b49\u5f0f (\u89e3\u7b54\u7de8)"},"content":{"rendered":"<p>\u3000\u7d76\u5bfe\u5024\u8a18\u53f7\u3067\u8868\u3055\u308c\u308b\u65b9\u7a0b\u5f0f\u3068\u4e0d\u7b49\u5f0f\u306f, \u4e00\u822c\u306b\u306f\u300c\u7d76\u5bfe\u5024\u8a18\u53f7\u5185\u306e\u6b63\u8ca0\u3067\u5834\u5408\u5206\u3051\u300d\u3092\u3059\u308b\u306e\u304c\u57fa\u672c\u3067\u3059\u304c, \u5834\u5408\u5206\u3051\u3092\u56de\u907f\u3057\u3066\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u305d\u306e\u65b9\u6cd5\u3092\u8003\u3048\u3066\u3044\u304d\u307e\u3059\u3002<br \/>\n\u3000<br \/>\n(1) \u4f8b\u3048\u3070, \u65b9\u7a0b\u5f0f \\(|\\,x\\,|=1\\) \u306e\u89e3\u306f, \\(x=\\pm 1\\) \u3067\u3059\u3002\u3053\u308c\u306b\u306a\u3089\u3063\u3066\u3069\u306e\u3088\u3046\u306a\u5b9f\u6570 \\(a\\) \u306e\u5834\u5408\u3067\u3082<br \/>\n\u3000\u3000\u300c\\(|\\,x\\,|=a\\) \u306e\u89e3\u306f \\(x=\\pm a\\)\u300d\u3000\\(\\cdots\\cdots\\) (\u2605)<br \/>\n\u3068\u306a\u308b\u304b\u3068\u8a00\u3048\u3070\u305d\u3046\u306f\u3044\u304d\u307e\u305b\u3093\u3002(\u2605) \u304c\u6210\u7acb\u3059\u308b\u306e\u306f \\(a\\geqq 0\\) \u306e\u3068\u304d\u3060\u3051\u3067\u3059\u3002\\(a\\lt 0\\) \u306e\u3068\u304d\u306f\u300c\u89e3\u306a\u3057\u300d\u306b\u306a\u3063\u3066\u3057\u307e\u3044\u307e\u3059\u3002<br \/>\n\u3000\u3053\u306e\u3053\u3068\u3092\u3075\u307e\u3048\u3066\u89e3\u304f\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<div style=\"border-style:solid;border-width:1px;padding:10px 5px 10px 20px;border-radius:10px;\">\n\u3000\u3000 \\(|\\,x^{3}-5x+2\\,| =x^{3}+1\\)<br \/>\n\u3000\\((\u5de6\u8fba)\\geqq 0\\) \u3088\u308a, \\(x^{3}+1\\geqq 0\\), \u3059\u306a\u308f\u3061,<br \/>\n\u3000\u3000\u3000\u3000\u3000 \\(x\\geqq -1\\)\u3000\u3000\\(\\cdots\\cdots\\,\\)\u2460<br \/>\n\u306e\u3082\u3068\u3067\u8003\u3048\u308b\u3002\u2460\u306e\u3068\u304d, \u4e0e\u3048\u3089\u308c\u305f\u65b9\u7a0b\u5f0f\u306f,<br \/>\n\u3000\u3000\u3000\u3000\u3000 \\(x^{3}-5x+2=\\pm (x^{3}+1)\\)<br \/>\n\u3068\u306a\u308b\u3002<br \/>\n(i) \\(x^{3}-5x+2=x^{3}+1\\) \u3092\u89e3\u304f\u3068,<br \/>\n\u3000\u3000\u3000\u3000\u3000 \\(x=\\displaystyle\\frac{1}{\\,5\\,}\\)<br \/>\n\u3068\u306a\u308a, \u3053\u308c\u306f\u2460\u3092\u6e80\u305f\u3059\u3002<\/p>\n<p>(ii) \\(x^{3}-5x+2=-(x^{3}+1)\\) \u3092\u89e3\u304f\u3068,<br \/>\n\u3000\u3000\u3000\u3000\u3000 \\(2x^{3}-5x+3=0\\)<br \/>\n\u3000\u3000\u3000\u3000\u3000 \\((x-1)(2x^{2}+2x-3)=0\\)<br \/>\n\u3000\u3000\u3000\u3000\u3000 \u2234\u3000\\(x=1\\), \\(\\displaystyle\\frac{\\,-1\\pm \\sqrt{7}\\,}{2}\\)<br \/>\n\u3053\u306e\u4e2d\u3067\u2460\u3092\u6e80\u305f\u3059\u3082\u306e\u306f,<br \/>\n\u3000\u3000\u3000\u3000\u3000 \\(x=1\\), \\(\\displaystyle\\frac{\\,-1+\\sqrt{7}\\,}{2}\\)<br \/>\n\u3067\u3042\u308b\u3002<br \/>\n\u3000\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u89e3\u306f,<br \/>\n\u3000\u3000\u3000\u3000\u3000 \\(x=\\displaystyle\\frac{1}{\\,5\\,}\\), 1, \\(\\displaystyle\\frac{\\,-1+\\sqrt{7}\\,}{2}\\)\u3000\u3000(\u7b54)\n<\/p><\/div>\n<p>(2) \u65b9\u7a0b\u5f0f\u306e\u5834\u5408\u3068\u540c\u69d8\u306b, \u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057\u3066\u4e0d\u7b49\u5f0f \\(|\\,x\\,|\\lt a\\) \u304c\u6210\u7acb\u3059\u308b\u306b\u306f\u307e\u305a \\(a\\geqq 0\\) \u3067\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3068\u8003\u3048\u3066\u3057\u307e\u3046\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c, \u6b21\u306e\u4f8b\u306f\u3069\u3046\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(a=1\\) \u306e\u5834\u5408<br \/>\n\u3000\u3000\\(|\\,x\\,|\\lt 1 \\iff -1\\lt x\\lt 1\\)<\/li>\n<li>\\(a=-1\\) \u306e\u5834\u5408<br \/>\n\u3000\u3000\\(|\\,x\\,|\\lt -1 \\iff -(-1)\\lt x\\lt -1\\)\n<\/li>\n<\/ul>\n<p>\\(a=1\\) \u306e\u5834\u5408\u306f,<br \/>\n\u3000\u3000\u3000\\(|\\,x\\,|\\lt a\\ \\iff -a\\lt x\\lt a\u3000\\cdots\\cdots\\) (\u2606)<br \/>\n\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u306f\u308f\u304b\u308a\u3084\u3059\u3044\u3067\u3059\u304c, \u5b9f\u306f \\(a=-1\\) \u306e\u5834\u5408\u3082 (\u2606) \u306f\u6210\u308a\u7acb\u3063\u3066\u3044\u307e\u3059\u3002\u306a\u305c\u306a\u3089, \\(a=-1\\) \u306e\u5834\u5408\u306f,<br \/>\n\u5de6\u8fba\u306f \\(|\\,x\\,|\\lt -1\\) \u3068\u306a\u308a\u3053\u308c\u3092\u6e80\u305f\u3059\u5b9f\u6570 \\(x\\) \u306f\u5b58\u5728\u3057\u307e\u305b\u3093\u3002<br \/>\n\u53f3\u8fba\u306f \\(-(-1)\\lt x\\lt -1\\) \u3068\u306a\u308a\u3053\u308c\u3092\u6e80\u305f\u3059\u5b9f\u6570 \\(x\\) \u3082\u5b58\u5728\u3057\u307e\u305b\u3093\u3002<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u306a\u308b\u304b\u3089\u3067\u3059\u3002\u3064\u307e\u308a, (\u2606) \u306f \\(a\\) \u306e\u6b63\u8ca0\u306b\u95a2\u308f\u3089\u305a\u3044\u3064\u3067\u3082\u4f7f\u3063\u3066\u3088\u3044\u5f0f\u306a\u306e\u3067\u3059\u3002<br \/>\n\u3000(1) \u3068 (2) \u306f\u65b9\u7a0b\u5f0f\u304b\u4e0d\u7b49\u5f0f\u304b\u306e\u9055\u3044\u3067\u3059\u304c, \u3053\u308c\u306f\u300c<strong>\u4e0d\u7b49\u5f0f\u306e\u65b9\u304c\u3084\u3055\u3057\u3044<\/strong>\u300d\u3068\u3044\u3063\u305f\u5927\u5909\u73cd\u3057\u3044\u5834\u5408\u306a\u306e\u3067\u3059\u3002<br \/>\n(\u6ce8) (\u2606) \u306e\u4e8b\u5b9f\u3092\u300c\u793a\u3057\u3066\u304b\u3089\u4f7f\u3048\u300d\u3068\u3059\u308b\u5834\u5408\u304c\u5168\u304f\u306a\u3044\u3068\u306f\u8a00\u3048\u307e\u305b\u3093\u3002<\/p>\n<p>\u3053\u306e\u4e0d\u7b49\u5f0f\u306e\u89e3\u306f\u6b21\u306e\u3088\u3046\u306b\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<br \/>\n\u3000\\(x^{3}+x^{2}-1\\) \u306e\u6b63\u8ca0\u306b\u95a2\u308f\u3089\u305a, \u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3067\u304d\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002<\/p>\n<div style=\"border-style:solid;border-width:1px;padding:10px 5px 10px 20px;border-radius:10px;\">\n\\(|\\, x^{3}+2x+2\\,|\\leqq x^{3}+x^{2}-1\\)\u3000\u3088\u308a,<br \/>\n\u3000\u3000\u3000\u3000 \\(-(x^{3}+x^{2}-1)\\leqq x^{3}+2x+2\\leqq x^{3}+x^{2}-1\\)<br \/>\n\u3059\u306a\u308f\u3061,<br \/>\n\u3000\u3000\u3000\u3000 \\(-(x^{3}+x^{2}-1)\\leqq x^{3}+2x+2\\ \\ \\cdots\\cdots\\) \u2460<br \/>\n\u304b\u3064<br \/>\n\u3000\u3000\u3000\u3000 \\(x^{3}+2x+2\\leqq x^{3}+x^{2}-1\\ \\ \\cdots\\cdots\\) \u2461<br \/>\n\u3092\u6e80\u305f\u3059 \\(x\\) \u304c\u4e0e\u3048\u3089\u308c\u305f\u4e0d\u7b49\u5f0f\u306e\u89e3\u3067\u3042\u308b\u3002<br \/>\n\u3000\u2460 \u3092\u89e3\u304f\u3068,<br \/>\n\u3000\u3000\u3000\u3000 \\(2x^{3}+x^{2}+2x+1\\geqq 0\\)<br \/>\n\u3000\u3000\u3000\u3000 \\((2x+1)(x^{2}+1)\\geqq 0\\)<br \/>\n\u3053\u3053\u3067, \u3059\u3079\u3066\u306e\u5b9f\u6570 \\(x\\) \u306b\u5bfe\u3057, \\(x^{2}+1\\gt 0\\) \u3067\u3042\u308b\u304b\u3089,<br \/>\n\u3000\u3000\u3000\u3000\u3000 \\(2x+1\\gt 0\\)<br \/>\n\u3000\u3000\u3000\u3000 \u2234\u3000\\(x\\gt -\\displaystyle\\frac{1}{\\,2\\,}\u3000\\cdots\\cdots\\) \u2462<br \/>\n\u3068\u306a\u308b\u3002<br \/>\n\u3000\u4e00\u65b9, \u2461\u3092\u89e3\u304f\u3068,<br \/>\n\u3000\u3000\u3000\u3000 \\(x^{2}-2x-3\\geqq 0\\)<br \/>\n\u3000\u3000\u3000\u3000 \\((x-3)(x+1)\\geqq 0\\)<br \/>\n\u3000\u3000\u3000\u3000 \\(x\\leqq -1\\) \u307e\u305f\u306f \\(x\\geqq 3\u3000\\cdots\\cdots\\) \u2463<br \/>\n\u3068\u306a\u308b\u3002<br \/>\n\u3000\u6c42\u3081\u308b\u89e3\u306f, \u2462 \u304b\u3064 \u2463 \u3060\u304b\u3089,<br \/>\n\u3000\u3000\u3000\u3000 \\(x\\geqq 3\\)\u3000\u3000\u3000(\u7b54)<br \/>\n\u3092\u5f97\u308b\u3002\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3000\u7d76\u5bfe\u5024\u8a18\u53f7\u3067\u8868\u3055\u308c\u308b\u65b9\u7a0b\u5f0f\u3068\u4e0d\u7b49\u5f0f\u306f, \u4e00\u822c\u306b\u306f\u300c\u7d76\u5bfe\u5024\u8a18\u53f7\u5185\u306e\u6b63\u8ca0\u3067\u5834\u5408\u5206\u3051\u300d\u3092\u3059\u308b\u306e\u304c\u57fa\u672c\u3067\u3059\u304c, \u5834\u5408\u5206\u3051\u3092\u56de\u907f\u3057\u3066\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u305d\u306e\u65b9\u6cd5\u3092\u8003\u3048\u3066\u3044\u304d\u307e\u3059\u3002 \u3000 (1) \u4f8b\u3048\u3070, \u65b9\u7a0b\u5f0f \\( [&hellip;]<\/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-1525","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\/1525","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=1525"}],"version-history":[{"count":3,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1525\/revisions"}],"predecessor-version":[{"id":1528,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1525\/revisions\/1528"}],"wp:attachment":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1525"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1525"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1525"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}