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一花引来百花开（5）：《几个精彩的平方和不等式》

2011-05-22 14:28:18| 分类：繁华 | 标签： |举报 |字号大中小订阅

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一花引来百花开（5）：《几个精彩的平方和不等式》 - sqing55 - sqing55S Blog

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$\frac{{{x^2} + {y^2}}}{{{{\left( {x - y} \right)}^2}}} + \frac{{{y^2} + {z^2}}}{{{{\left( {y - z} \right)}^2}}} + \frac{{{z^2...$

与 ${\left( {\frac{{x + y}}{{x - y}}} \right)^2} + {\left( {\frac{{y + z}}{{y - z}}} \right)^2} + {\left( {\frac{{z + x}}{{z - x}...$ 等价。

在
${\left( {\frac{{x + y}}{{x - y}}} \right)^2} + {\left( {\frac{{y + z}}{{y - z}}} \right)^2} + {\left( {\frac{{z + x}}{{z - x}...$ 两边加3，即得

$\frac{{{x^2} + {y^2}}}{{{{\left( {x - y} \right)}^2}}} + \frac{{{y^2} + {z^2}}}{{{{\left( {y - z} \right)}^2}}} + \frac{{{z^2...$ 。

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