\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b\u3068\u304d\u3001\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u7b49\u5f0f\u304c\u5e38\u306b\u6210\u308a\u7acb\u3064\u3068\u3044\u3046\u306e\u306f\u3001\u6052\u7b49\u5f0f\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b\u306e\u3068\u610f\u5473\u304c\u540c\u3058\u3067\u3059\u3002<\/p>\n
\u8a3c\u660e\u306e\u65b9\u6cd5\u306f\u6c7a\u307e\u3063\u3066\u3044\u308b\u305f\u3081\u3001\u5177\u4f53\u7684\u306a\u8a3c\u660e\u65b9\u6cd5\u3092\u899a\u3048\u307e\u3057\u3087\u3046\u3002\u306a\u304a\u3001\u8a3c\u660e\u65b9\u6cd5\u306f\u96e3\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u6761\u4ef6\u4ed8\u304d\u306e\u8a3c\u660e\u3092\u3059\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u304c\u3001\u6761\u4ef6\u3092\u5229\u7528\u3057\u3066\u6052\u7b49\u5f0f\u3092\u8a08\u7b97\u3059\u308c\u3070\u8a3c\u660e\u3067\u304d\u307e\u3059\u3002<\/p>\n
\u306a\u304a\u7b49\u5f0f\u306e\u8a3c\u660e\u3067\u306f\u3001\u6bd4\u4f8b\u5f0f\uff08\u5206\u6570\u5f0f\uff09\u3092\u542b\u3080\u8a3c\u660e\u554f\u984c\u3092\u89e3\u304b\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u8a18\u53f7\u3092\u5229\u7528\u3057\u3066\u8a3c\u660e\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n
\u305d\u308c\u3067\u306f\u3001\u5177\u4f53\u7684\u306b\u3069\u306e\u3088\u3046\u306b\u8003\u3048\u3066\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3059\u308b\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n
\u6052\u7b49\u5f0f\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b\u306b\u306f\u3001\u4e3b\u306b\u4ee5\u4e0b\u306e3\u3064\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n
\u3053\u306e\u3046\u3061\u3001\u300c\u5de6\u8fba\\(-\\)\u53f3\u8fba\\(=0\\)\u3092\u8a18\u3059\u300d\u304c\u5229\u7528\u3055\u308c\u308b\u3053\u3068\u306f\u307b\u3068\u3093\u3069\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u306e\u305f\u3081\u5de6\u8fba\u307e\u305f\u306f\u53f3\u8fba\u3092\u5909\u5f62\u3057\u3001\u6052\u7b49\u5f0f\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n
\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u5b66\u3076\u3068\u304d\u3001\u5b9f\u969b\u306b\u554f\u984c\u3092\u89e3\u304f\u3068\u7406\u89e3\u3057\u3084\u3059\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u5f0f\u304c\u6052\u7b49\u5f0f\u3067\u3042\u308b\u3068\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n
\\(x^3+y^3=(x\uff0by)^3\u2212\uff13xy(x\uff0by)\\)<\/p>\n
\u53f3\u8fba\u3092\u5909\u5f62\u3057\u3001\u5de6\u8fba\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n
\\((x\uff0by)^3\u2212\uff13xy(x\uff0by)\\)<\/p>\n
\\(=x^3+3x^2y+3xy^2+y^3\\)\\(-3x^2y-3xy^2\\)<\/p>\n
\\(=x^3+y^3=\\)\u5de6\u8fba<\/p>\n
\u3053\u3046\u3057\u3066\u53f3\u8fba\u3092\u5909\u5f62\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5de6\u8fba\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3068\u8a3c\u660e\u3067\u304d\u307e\u3059\u3002<\/p>\n
\u306a\u304a\u5de6\u8fba\u3068\u53f3\u8fba\u3092\u5909\u5f62\u3057\u3001\u540c\u3058\u5f0f\u3092\u4f5c\u308b\u65b9\u6cd5\u3067\u3042\u3063\u3066\u3082\u7b49\u5f0f\u306e\u8a3c\u660e\u304c\u53ef\u80fd\u3067\u3059\u3002\u6b21\u306f\u4ee5\u4e0b\u306e\u5f0f\u304c\u6052\u7b49\u5f0f\u3067\u3042\u308b\u3068\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n
\\((1+x)^3=1+x\\)\\(+x(1+x)\\)\\(+x(1+x)^2\\)<\/p>\n
\u4e21\u65b9\u306e\u5f0f\u304c\u8907\u96d1\u306a\u306e\u3067\u3001\u5de6\u8fba\u3068\u53f3\u8fba\u3092\u305d\u308c\u305e\u308c\u5c55\u958b\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u540c\u3058\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n
\u30fb\u5de6\u8fba\u306e\u8a08\u7b97<\/strong><\/p>\n \\((1+x)^3\\)<\/p>\n \\(=1+3x+3x^2+x^3\\)<\/p>\n \u30fb\u53f3\u8fba\u306e\u8a08\u7b97<\/strong><\/p>\n \\(1+x+x(1+x)+x(1+x)^2\\)<\/p>\n \\(=1+x+x+x^2+x+2x^2+x^3\\)<\/p>\n \\(=1+3x+3x^2+x^3\\)<\/p>\n \u3053\u3046\u3057\u3066\u5de6\u8fba\u3068\u53f3\u8fba\u304c\u540c\u3058\u5f0f\u306b\u306a\u308b\u3068\u78ba\u8a8d\u3067\u304d\u3001\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n \u306a\u304a\u7b49\u5f0f\u306e\u8a3c\u660e\u3067\u306f\u3001\u6761\u4ef6\u304c\u52a0\u3048\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u7279\u5b9a\u306e\u6761\u4ef6\u306e\u3068\u304d\u306b\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3064\u306e\u3067\u3059\u3002\u6761\u4ef6\u4ed8\u304d\u306e\u7b49\u5f0f\u306e\u8a3c\u660e\u3067\u306f\u3001\u6761\u4ef6\u3092\u5229\u7528\u3057\u3066\u5de6\u8fba\u3068\u53f3\u8fba\u304c\u7b49\u3057\u3044\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n \u305d\u308c\u3067\u306f\\(a+b+c=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 \u6761\u4ef6\u5f0f\u3092\u5229\u7528\u3057\u3001\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3053\u3068\u3067\u5de6\u8fba\u3068\u53f3\u8fba\u304c\u540c\u3058\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3059\u3002\\(a+b+c=0\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(a=-b-c\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\\(a=-b-c\\)\u3092\u5de6\u8fba\u306e\u5f0f\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(a^3+b^3+c^3-3abc\\)<\/p>\n \\(=(-b-c)^3+b^3+c^3-3bc(-b-c)\\)<\/p>\n \\(=(-b^3-3b^2c-3bc^2-c^3)\\)\\(+b^3+c^3\\)\\(+3b^2c+3bc^2\\)<\/p>\n \\(=0\\)<\/p>\n \u3053\u3046\u3057\u3066\u3001\u6761\u4ef6\u4ed8\u304d\u306e\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n \u7b49\u5f0f\u306e\u8a3c\u660e\u3067\u306f\u6bd4\u4f8b\u5f0f\u3092\u53d6\u308a\u6271\u3046\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u6bd4\u4f8b\u5f0f\u3092\u542b\u3080\u7b49\u5f0f\u306e\u8a3c\u660e\u3067\u306f\u3084\u308a\u65b9\u304c\u3042\u308b\u305f\u3081\u3001\u4e8b\u524d\u306b\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u6bd4\u4f8b\u5f0f\uff08\u5206\u6570\u5f0f\uff09\u306b\u5bfe\u3057\u3066\\(=k\\)\u3068\u8a2d\u5b9a\u3057\u307e\u3059\u3002<\/p>\n \u4f8b\u3048\u3070\\(\\displaystyle\\frac{a}{b}=\\displaystyle\\frac{c}{d}\\)\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u7b49\u5f0f\u3092\u3069\u306e\u3088\u3046\u306b\u8a3c\u660e\u3059\u308c\u3070\u3044\u3044\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n \u6bd4\u4f8b\u5f0f\u3067\u306f\u6bd4\u7387\u304c\u540c\u3058\u3067\u3059\u3002\u305d\u3053\u3067\u3001\\(\\displaystyle\\frac{a}{b}=\\displaystyle\\frac{c}{d}=k\\)\u3068\u8a2d\u5b9a\u3057\u307e\u3057\u3087\u3046\u3002\u3064\u307e\u308a\\(a=bk\\)\u3067\u3042\u308a\u3001\\(c=dk\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u5de6\u8fba\u3068\u53f3\u8fba\u3092\u305d\u308c\u305e\u308c\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n \u30fb\u5de6\u8fba\u306e\u8a08\u7b97<\/strong><\/p>\n \\(\\displaystyle\\frac{a^2+c^2}{a^2-c^2}\\)<\/p>\n \\(=\\displaystyle\\frac{b^2k^2+d^2k^2}{b^2k^2-d^2k^2}\\)<\/p>\n \\(=\\displaystyle\\frac{b^2+d^2}{b^2-d^2}\\)<\/p>\n \u30fb\u53f3\u8fba\u306e\u8a08\u7b97<\/strong><\/p>\n \\(\\displaystyle\\frac{ab+cd}{ab-cd}\\)<\/p>\n \\(=\\displaystyle\\frac{b^2k+d^2k}{b^2k-d^2k}\\)<\/p>\n \\(=\\displaystyle\\frac{b^2+d^2}{b^2-d^2}\\)<\/p>\n \u5de6\u8fba\u3068\u53f3\u8fba\u304c\u540c\u3058\u5f0f\u306b\u306a\u3063\u305f\u305f\u3081\u3001\u7b49\u5f0f\u306e\u8a3c\u660e\u3092\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u6bd4\u4f8b\u5f0f\u3092\u542b\u3080\u7b49\u5f0f\u306e\u8a08\u7b97\u3067\u306f\u3001\u3053\u306e\u3088\u3046\u306b\u8a18\u53f7\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \u3053\u3053\u307e\u3067\u3001\u3059\u3079\u3066\u306e\u5024\u304c\u5f53\u3066\u306f\u307e\u308b\u5f0f\u306b\u3064\u3044\u3066\u78ba\u8a8d\u3057\u307e\u3057\u305f\u3002\u4e00\u65b9\u3001\u3059\u3079\u3066\u306e\u5024\u3067\u306f\u306a\u304f\u3001\u4e00\u90e8\u306e\u5024\u304c\u5f53\u3066\u306f\u307e\u308b\u5834\u5408\u306f\u3069\u306e\u3088\u3046\u306b\u8a3c\u660e\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u3064\u307e\u308a\u3001\u5c11\u306a\u304f\u3068\u3082\u4e00\u3064\u306e\u5024\u304c\u5f53\u3066\u306f\u307e\u308b\u30b1\u30fc\u30b9\u3092\u8003\u3048\u308b\u306e\u3067\u3059\u3002<\/p>\n \u3069\u306e\u3088\u3046\u306b\u3059\u308c\u3070\u3001\u5c11\u306a\u304f\u3068\u30821\u3064\u304c\u5f53\u3066\u306f\u307e\u308b\u3068\u8a3c\u660e\u3067\u304d\u308b\u306e\u3067\u3057\u3087\u304b\u3002\u4f8b\u3048\u3070\\(AB=0\\)\u306e\u5834\u5408\u3001A\u307e\u305f\u306fB\u306e\u3046\u3061\u3001\u3069\u3061\u3089\u304b\u304c0\u3067\u3059\u3002\u3064\u307e\u308a\\(AB=0\\)\u3068\u306a\u308b\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u308c\u3070\u3001A\u3068B\u306e\u3046\u3061\u5c11\u306a\u304f\u3068\u3082\u3069\u3061\u3089\u304b\u4e00\u65b9\u306f0\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n \u307e\u305f\\((A+2)(B+2)=0\\)\u306e\u5834\u5408\u3001A\u3068B\u306e\u3046\u3061\u5c11\u306a\u304f\u3068\u3082\u3069\u3061\u3089\u304b\u4e00\u65b9\u306f\u7b54\u3048\u304c-2\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u65b9\u91dd\u306b\u3088\u3063\u3066\u8a3c\u660e\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n \u5c11\u306a\u304f\u3068\u3082\u4e00\u3064\u306f\u5024\u304c1\u306b\u306a\u308b\u305f\u3081\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u5f0f\u306b\u306a\u308c\u3070\u3044\u3044\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n \u305d\u3053\u3067\u3001\\(P=(a-1)(b-1)(c-1)\\)\u3068\u3057\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(P=(a-1)(b-1)(c-1)\\)<\/p>\n \\(=(ab-a-b+1)(c-1)\\)<\/p>\n \\(=abc-ab-ca+a-bc+b\\)\\(+c-1\\)<\/p>\n \\(=(ab+bc+ca)-ab-bc-ca\\)\\(+(a+b+c)\\)\\(-1\\)<\/p>\n \\(=0\\)<\/p>\n \u3053\u3046\u3057\u3066\\((a-1)(b-1)(c-1)=0\\)\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u3001\\(a\\)\u3001\\(b\\)\u3001\\(c\\)\u306e\u3046\u3061\u5c11\u306a\u304f\u3068\u3082\u4e00\u3064\u306f\u5024\u304c1\u3067\u3042\u308b\u3068\u8a3c\u660e\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n \u5c11\u306a\u304f\u3068\u3082\u4e00\u3064\u304c\u5f53\u3066\u306f\u307e\u308b\u30b1\u30fc\u30b9\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306a\u5f0f\u3092\u4f5c\u3089\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u306e\u304b\u3042\u306a\u305f\u304c\u7406\u89e3\u3057\u3066\u304a\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u524d\u63d0\u6761\u4ef6\u304b\u3089\u7b54\u3048\u3092\u8a18\u3057\u3001\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n 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