\u7b49\u5f0f\u306e\u8a3c\u660e\u3088\u308a\u3082\u96e3\u3057\u3044\u8a3c\u660e\u554f\u984c\u304c\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3067\u3059\u3002\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3059\u308b\u3068\u304d\u3001\u5927\u5c0f\u95a2\u4fc2\u3092\u5229\u7528\u3057\u305f\u308a\u3001\u7d2f\u4e57\u3092\u5229\u7528\u3057\u305f\u308a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4e0d\u7b49\u5f0f\u306e\u6027\u8cea\u3092\u7406\u89e3\u3057\u3066\u3001\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n
\u306a\u304a\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3067\u306f\u3001\u5f0f\u306b\u7d76\u5bfe\u5024\u3092\u542b\u3080\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u7d76\u5bfe\u5024\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u3067\u3042\u3063\u3066\u3082\u4e0d\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u8a3c\u660e\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n
\u307e\u305f\u4e0d\u7b49\u5f0f\u304c\u95a2\u308f\u308b\u8a3c\u660e\u554f\u984c\u3067\u306f\u3001\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u3082\u5229\u7528\u3055\u308c\u307e\u3059\u3002\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u306e\u95a2\u4fc2\u306f\u516c\u5f0f\u3068\u3057\u3066\u899a\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u6700\u5927\u5024\u307e\u305f\u306f\u6700\u5c0f\u5024\u3092\u5f97\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n
\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3059\u308b\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n
\u4e0d\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u8a3c\u660e\u3057\u305f\u3044\u3068\u304d\u3001\u6700\u3082\u4e00\u822c\u7684\u306a\u65b9\u6cd5\u3068\u3057\u3066\u3001\u5f15\u304d\u7b97\u3092\u3059\u308b\u8a3c\u660e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\\(A>B\\)\u3092\u8a3c\u660e\u3059\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3044\u3044\u3067\u3057\u3087\u3046\u304b\u3002\u3082\u3057\\(A-B>0\\)\u3067\u3042\u308b\u3068\u308f\u304b\u308c\u3070\u3001\u4e0d\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n \u5b9f\u969b\u306b\u8a3c\u660e\u554f\u984c\u3092\u89e3\u304f\u3068\u3001\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u65b9\u6cd5\u3092\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n \u5927\u5c0f\u95a2\u4fc2\u3092\u5229\u7528\u3057\u3066\u8a3c\u660e\u3059\u308c\u3070\u3044\u3044\u305f\u3081\u3001\u5f15\u304d\u7b97\u3092\u5229\u7528\u3057\u30660\u3088\u308a\u3082\u5927\u304d\u3044\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n \\(ab+1-a-b\\)<\/p>\n \\(=a(b-1)-(b-1)\\)<\/p>\n \\(=(a-1)(b-1)\\)<\/p>\n \\(a>1\\)\u3001\\(b>1\\)\u3067\u3042\u308b\u305f\u3081\u3001\\((a-1)(b-1)>0\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(ab+1>a+b\\)\u3068\u8a3c\u660e\u3067\u304d\u307e\u3057\u305f\u3002\u5927\u5c0f\u95a2\u4fc2\u3092\u5229\u7528\u3067\u304d\u308b\u5834\u5408\u3001\u5f15\u304d\u7b97\u306b\u3088\u3063\u3066\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \u305f\u3060\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u5927\u5c0f\u95a2\u4fc2\u3092\u5229\u7528\u3057\u3066\u3082\u4e0d\u7b49\u5f0f\u3092\u8a3c\u660e\u3067\u304d\u306a\u3044\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u7d2f\u4e57\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3057\u307e\u3057\u3087\u3046\u3002\u5b9f\u6570\u3092\u4e8c\u4e57\u3059\u308b\u5834\u5408\u3001\u5fc5\u305a\u5024\u306f\u6b63\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u6027\u8cea\u3092\u5229\u7528\u3057\u3066\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n \u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u4e0d\u7b49\u5f0f\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \u65b9\u91dd\u3068\u3057\u3066\u3001\u5f15\u304d\u7b97\u3092\u5229\u7528\u3059\u308b\u306e\u306f\u540c\u3058\u3067\u3059\u3002\u305d\u308c\u306b\u52a0\u3048\u3066\u3001\u56e0\u6570\u5206\u89e3\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u4e8c\u4e57\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/span>\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n \\((x^2+16y^2+1)-8xy\\)<\/p>\n \\(=x^2-8xy+16y^2+1\\)<\/p>\n \\(=(x-4y)^2+1>0\\)<\/p>\n \u4e8c\u4e57\u3059\u308b\u5834\u5408\u3001\u5fc5\u305a\u5024\u306f\u30bc\u30ed\u4ee5\u4e0a\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(x^2+16y^2+1>8xy\\)\u3067\u3042\u308b\u3068\u8a3c\u660e\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n \u3053\u3053\u307e\u3067\u3001\u6574\u6570\u306b\u95a2\u3059\u308b\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u554f\u984c\u3092\u89e3\u3044\u3066\u304d\u307e\u3057\u305f\u3002\u305d\u308c\u3067\u306f\u3001\u5e73\u65b9\u6839\u306a\u3069\u306e\u7121\u7406\u6570\u3092\u542b\u3080\u5834\u5408\u306f\u3069\u306e\u3088\u3046\u306b\u8a3c\u660e\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n \u4e8c\u4e57\u3059\u308b\u3068\u3001\u5e73\u65b9\u6839\u3092\u53d6\u308a\u53bb\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u4e8c\u4e57\u3057\u3066\u3082\u5927\u5c0f\u95a2\u4fc2\u306f\u5909\u5316\u3057\u307e\u305b\u3093\u3002\u4f8b\u3048\u3070\\(a>b\\)\u306e\u5834\u5408\u3001\\(a^2>b^2\\)\u3067\u3059\u3002\u3053\u306e\u6027\u8cea\u3092\u5229\u7528\u3057\u3066\u4e0d\u7b49\u5f0f\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u5f0f\u3092\u4e8c\u4e57\u3057\u305f\u5f8c\u306b\u5f15\u304d\u7b97\u3092\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n \u305d\u308c\u3067\u306f\\(a>0\\)\u304b\u3064\\(b>0\\)\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \u3053\u306e\u4e0d\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3064\u5834\u5408\u3001\u4e21\u8fba\u3092\u4e8c\u4e57\u3057\u3066\u3082\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/span>\u307e\u305f\u3001\u5927\u5c0f\u95a2\u4fc2\uff08\u5f15\u304d\u7b97\uff09\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u4e0d\u7b49\u5f0f\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n \\((\\sqrt{a}+\\sqrt{b})^2-\\sqrt{a+b}^2\\)<\/p>\n \\(=(a+2\\sqrt{ab}+b)-(a+b)\\)<\/p>\n \\(=2\\sqrt{ab}>0\\)<\/p>\n \u5de6\u8fba\u304b\u3089\u53f3\u8fba\u3092\u5f15\u304f\u30680\u3088\u308a\u5927\u304d\u3044\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u305f\u3081\u3001\u4e0d\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3068\u8a3c\u660e\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n \u6b21\u306b\u3001\u7d76\u5bfe\u5024\u3092\u542b\u3080\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u554f\u984c\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u5834\u5408\u5206\u3051\u3092\u3059\u308b\u3053\u3068\u3067\u8a3c\u660e\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u3059\u304c\u3001\u5f0f\u306b\u542b\u307e\u308c\u308b\u7d76\u5bfe\u5024\u304c\u591a\u3044\u5834\u5408\u3001\u5834\u5408\u5206\u3051\u306f\u826f\u3044\u30a2\u30a4\u30c7\u30a3\u30a2\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u307b\u304b\u306e\u65b9\u6cd5\u306b\u3088\u3063\u3066\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \u7d76\u5bfe\u5024\u3092\u542b\u3080\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3067\u306f\u3001\u4e8b\u524d\u306b\u7406\u89e3\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u5185\u5bb9\u304c2\u3064\u3042\u308a\u307e\u3059\u3002\u307e\u305a\u3001\\(|A|\u2267A\\)\u3068\u306a\u308b\u3053\u3068\u3092\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002A\u304c\u6b63\u306e\u5024\u3067\u3042\u308c\u3070\\(|A|=A\\)\u3067\u3059\u3002\u307e\u305fA\u304c\u8ca0\u306e\u5024\u3067\u3042\u308c\u3070\u3001\\(|A|>A\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(|A|\u2267A\\)\u3067\u3059\u3002<\/p>\n \u307e\u305f\u4e8c\u4e57\u3059\u308b\u3068\u5fc5\u305a\u6b63\u306e\u5024\u306b\u306a\u308b\u305f\u3081\u3001\\(|A|^2=A^2\\)\u3067\u3059\u3002\u57fa\u672c\u7684\u306a\u5185\u5bb9\u3067\u306f\u3042\u308a\u307e\u3059\u304c\u3001\u3053\u308c\u3089\u306e\u5185\u5bb9\u3092\u7406\u89e3\u3057\u3066\u3001\u7d76\u5bfe\u5024\u3092\u542b\u3080\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u6b21\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \u5f15\u304d\u7b97\u3060\u3051\u3067\u306f\u8a3c\u660e\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u7d2f\u4e57\u3057\u305f\u5f8c\u306b\u5f15\u304d\u7b97\u3092\u3057\u307e\u3057\u3087\u3046\u3002\u307e\u305f\u3001\u5148\u307b\u3069\u89e3\u8aac\u3057\u305f\u7d76\u5bfe\u5024\u306e\u6027\u8cea\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u305d\u3046\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n \\((|a|+|b|)^2-|a+b|^2\\)<\/p>\n \\(=(a^2+2|a||b|+b^2)-(a+b)^2\\)<\/p>\n \\(=(a^2+2|a||b|+b^2)\\)\\(-(a^2+2ab+b^2)\\)<\/p>\n \\(=2|a||b|-2ab\u22670\\)<\/p>\n \u3053\u3046\u3057\u3066\u3001\u5de6\u8fba\u306e\u4e8c\u4e57\u304b\u3089\u53f3\u8fba\u306e\u4e8c\u4e57\u3092\u5f15\u304f\u3053\u3068\u306b\u3088\u308a\u30010\u4ee5\u4e0a\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u305d\u306e\u305f\u3081\u3001\\(|a|+|b|\u2267|a+b|\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n \u306a\u304a\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u306b\u95a2\u3059\u308b\u5185\u5bb9\u306b\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u306e\u5927\u5c0f\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u304c\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u3067\u3059\u3002<\/p>\n \u307e\u305f\\(a\\)\u3068\\(b\\)\u306e\u4e21\u65b9\u3068\u3082\u6b63\u306e\u6570\u3067\u3042\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n \u8a3c\u660e\u65b9\u6cd5\u306f\u7c21\u5358\u3067\u3042\u308a\u3001\u4e8c\u4e57\u3057\u305f\u5f8c\u306b\u5f15\u304d\u7b97\u3092\u3057\u307e\u3057\u3087\u3046\u3002\\(\\displaystyle\\frac{a+b}{2}\u2267\\sqrt{ab}\\)\u3088\u308a\u3001\\(a+b\u22672\\sqrt{ab}\\)\u3068\u8003\u3048\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n \\((a+b)^2-(2\\sqrt{ab})^2\\)<\/p>\n \\(=(a^2+2ab+b^2)-4ab\\)<\/p>\n \\(=a^2-2ab+b^2\\)<\/p>\n \\(=(a-b)^2\u22670\\)<\/p>\n \u3053\u3046\u3057\u3066\u3001\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u306e\u5927\u5c0f\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u306a\u304a\u3001\\(\\displaystyle\\frac{a+b}{2}=\\sqrt{ab}\\)\u3068\u306a\u308b\u306e\u306f\\(a=b\\)\u306e\u3068\u304d\u3067\u3059\u3002<\/p>\n \u3061\u306a\u307f\u306b\u3001\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u306e\u5927\u5c0f\u95a2\u4fc2\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u3001\\(a+b\u22672\\sqrt{ab}\\)\u3068\u899a\u3048\u3066\u3082\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u3002<\/span><\/p>\n \u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306a\u3068\u304d\u306b\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u306e\u5927\u5c0f\u95a2\u4fc2\u3092\u5229\u7528\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u9006\u6570\u306e\u95a2\u4fc2\u306b\u306a\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u306e\u5927\u5c0f\u95a2\u4fc2\u3092\u5229\u7528\u3067\u304d\u306a\u3044\u304b\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/span>\u4f8b\u3048\u3070\\(x\\)\u3068\\(\\displaystyle\\frac{1}{x}\\)\u306f\u9006\u6570\u306e\u95a2\u4fc2\u3067\u3059\u3002\u9006\u6570\u3067\u3042\u308c\u3070\u3001\u76f8\u4e57\u5e73\u5747\u306e\u8a08\u7b97\u304c\u7c21\u5358\u3067\u3059\u3002<\/p>\n \u305d\u308c\u3067\u306f\u3001\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u306e\u5927\u5c0f\u95a2\u4fc2\u3092\u5229\u7528\u3057\u3066\u5f0f\u306e\u8a3c\u660e\u3092\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\\(a>0\\)\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \u76f8\u52a0\u5e73\u5747\u3092\u76f8\u4e57\u5e73\u5747\u3078\u5909\u63db\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n \\(3a+\\displaystyle\\frac{2}{a}\\)<\/p>\n \\(\u22672\\sqrt{3a\u00d7\\displaystyle\\frac{2}{a}}\\)<\/p>\n \\(=2\\sqrt{6}\\)<\/p>\n \u3053\u3046\u3057\u3066\u3001\\(3a+\\displaystyle\\frac{2}{a}\u22672\\sqrt{6}\\)\u3067\u3042\u308b\u3068\u8a3c\u660e\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n \u306a\u304a\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u3092\u5229\u7528\u3059\u308b\u5834\u5408\u3001\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u6700\u5927\u5024\u307e\u305f\u306f\u6700\u5c0f\u5024\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n \u4f8b\u3048\u3070\u5148\u307b\u3069\u3001\\(3a+\\displaystyle\\frac{2}{a}\u22672\\sqrt{6}\\)\u306e\u95a2\u4fc2\u3092\u8a3c\u660e\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u3064\u307e\u308a\u3001\\(a>0\\)\u306e\u3068\u304d\u3001\u6700\u5c0f\u5024\u306f\\(2\\sqrt{6}\\)\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n \u306a\u304a\u30012\u30f5\u6240\u4ee5\u4e0a\u3067\u76f8\u52a0\u5e73\u5747\u3092\u76f8\u4e57\u5e73\u5747\u3078\u5909\u63db\u3059\u308b\u5834\u5408\u306f\u6ce8\u610f\u3057\u307e\u3057\u3087\u3046\u3002<\/span>\u5b9f\u969b\u306e\u7b54\u3048\u3068\u306f\u7570\u306a\u308b\u30b1\u30fc\u30b9\u304c\u3042\u308b\u304b\u3089\u3067\u3059\u3002\u305d\u308c\u3067\u306f\\(a>0\\)\u3001\\(b>0\\)\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u5f0f\u306e\u6700\u5c0f\u5024\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n \u305d\u308c\u305e\u308c\u306e\u304b\u3063\u3053\u306b\u5bfe\u3057\u3066\u3001\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u306e\u5927\u5c0f\u95a2\u4fc2\u3092\u9069\u7528\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n \\(\\left(a+\\displaystyle\\frac{4}{b}\\right)\\left(b+\\displaystyle\\frac{1}{a}\\right)\\)<\/p>\n \\(\u22672\\sqrt{a\u00d7\\displaystyle\\frac{4}{b}}\u00d72\\sqrt{b\u00d7\\displaystyle\\frac{1}{a}}\\)<\/p>\n \\(=8\\)<\/p>\n \u305f\u3060\u3001\u7b54\u3048\u306f8\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u306e\u8a08\u7b97\u306e\u4f55\u304c\u9593\u9055\u3063\u3066\u3044\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4e00\u3064\u76ee\u306e\u304b\u3063\u3053\u5185\u304c\u6700\u5c0f\u5024\u306b\u306a\u308b\u306e\u306f\\(a=\\displaystyle\\frac{4}{b}\\)\u306e\u3068\u304d\u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(ab=4\\)\u306e\u3068\u304d\u306b\u6700\u5c0f\u5024\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n \u307e\u305f\u4e8c\u3064\u76ee\u306e\u304b\u3063\u3053\u5185\u304c\u6700\u5c0f\u5024\u306b\u306a\u308b\u305f\u3081\u306b\u306f\u3001\\(b=\\displaystyle\\frac{1}{a}\\)\u306e\u3068\u304d\u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(ab=1\\)\u306e\u3068\u304d\u306b\u6700\u5c0f\u5024\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n \u3057\u304b\u3057\u3001\\(ab=4\\)\u3068\\(ab=1\\)\u3092\u540c\u6642\u306b\u6e80\u305f\u3059\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002<\/span>\u305d\u306e\u305f\u3081\u3001\u6700\u5c0f\u5024\u304c8\u306b\u306a\u308b\u3053\u3068\u306f\u306a\u3044\u306e\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u5148\u307b\u3069\u306e\u5f0f\u3092\u5c55\u958b\u3057\u305f\u5f8c\u306b\u76f8\u52a0\u5e73\u5747\u3092\u76f8\u4e57\u5e73\u5747\u306b\u5909\u63db\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n \\(\\left(a+\\displaystyle\\frac{4}{b}\\right)\\left(b+\\displaystyle\\frac{1}{a}\\right)\\)<\/p>\n \\(=ab+1+4+\\displaystyle\\frac{4}{ab}\\)<\/p>\n \\(=ab+\\displaystyle\\frac{4}{ab}+5\\)<\/p>\n \u305d\u3053\u3067\u3001\u3053\u306e\u5f0f\u306b\u5bfe\u3057\u3066\u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u306e\u5927\u5c0f\u95a2\u4fc2\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(ab+\\displaystyle\\frac{4}{ab}+5\\)<\/p>\n \\(\u22672\\sqrt{ab\u00d7\\displaystyle\\frac{4}{ab}}+5\\)<\/p>\n \\(=9\\)<\/p>\n \u3053\u3046\u3057\u3066\u3001\u6700\u5c0f\u5024\u306f9\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u307e\u305f\u3001\\(ab=\\displaystyle\\frac{4}{ab}\\)\u306e\u3068\u304d\u3001\u6700\u5c0f\u5024\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(ab=\\displaystyle\\frac{4}{ab}\\)<\/p>\n \\((ab)^2=4\\)<\/p>\n \\(ab=2\\)<\/p>\n \u3064\u307e\u308a\\(ab=2\\)\u306e\u3068\u304d\u3001\u6700\u521d\u50249\u3068\u306a\u308a\u307e\u3059\u3002\u307e\u305f\u76f8\u52a0\u5e73\u5747\u3092\u76f8\u4e57\u5e73\u5747\u3078\u5909\u66f4\u3059\u308b\u5834\u6240\u306f\u4e00\u3064\u3067\u3042\u308b\u305f\u3081\u3001\u7b54\u3048\u304c\u77db\u76fe\u3059\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n \u76f8\u52a0\u5e73\u5747\u3068\u76f8\u4e57\u5e73\u5747\u306e\u5927\u5c0f\u95a2\u4fc2\u3067\u306f\u3001\u7b49\u53f7\u304c\u6210\u7acb\u3059\u308b\u305f\u3081\u306e\u6761\u4ef6\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u6761\u4ef6\u3068\u5408\u81f4\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u30012\u30f5\u6240\u3067\u76f8\u52a0\u5e73\u5747\u3092\u76f8\u4e57\u5e73\u5747\u3078\u5909\u63db\u3059\u308b\u5834\u5408\u306f\u7b49\u53f7\u6210\u7acb\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \u6570\u5b66\u3067\u306f\u8a3c\u660e\u554f\u984c\u304c\u51fa\u984c\u3055\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3067\u306f\u5927\u5c0f\u95a2\u4fc2\u3092\u5229\u7528\u3057\u305f\u308a\u3001\u5f0f\u3092\u4e8c\u4e57\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u4e0d\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \u306a\u304a\u4e0d\u7b49\u5f0f\u3092\u542b\u3080\u5f0f\u306b\u306f\u3001\u7d76\u5bfe\u5024\u3092\u542b\u3080\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u57fa\u672c\u7684\u306a\u5185\u5bb9\u3067\u306f\u3042\u3063\u3066\u3082\u3001\u7d76\u5bfe\u5024\u306e\u304b\u3051\u7b97\u3084\u4e8c\u4e57\u3092\u3059\u308b\u3068\u304d\u3001\u3069\u306e\u3088\u3046\u306b\u5024\u304c\u5909\u5316\u3059\u308b\u306e\u304b\u628a\u63e1\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n 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