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$$
\eqalign{
& {\cal 设}x,y,z,a,b,c{\cal 为}{\cal 正}{\cal 数}{\text{ ,}}\max (x,y,z) \geqslant \min (a,b,c){\text{.}} \cr
& \max (a,b,c) \geqslant \min (x,y,z){\text{.}}{\cal 求}{\cal 证}: \cr
& \frac{{b^2 }}
{a} + \frac{{c^2 }}
{b} + \frac{{a^2 }}
{c} + \frac{{y^2 }}
{x} + \frac{{z^2 }}
{y} + \frac{{x^2 }}
{z} \geqslant {\text{ }}\sqrt {6(a^2 + b^2 + c^2 + x^2 + y^2 + z^2 )} \cr
& Wanhuihua{\text{ 20170306}} \cr}
$$
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