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Let $a, b, c$ be nonzero numbers and $x, y, z$ be arbitrary positive numbers with $x+$ $y+z=3$. Prove that inequality
$\frac{3}{2} \sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}} \geq \frac{x}{1+a^2}+\frac{y}{1+b^2}+\frac{z}{1+c^2} .$
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