camp exam problem-11

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camp exam problem-11

Unread post by nafistiham » Fri Nov 04, 2011 10:53 pm

Let $a,b,c,x,y,z$ be positive numbers such that $a \geq b \geq c$ and $x \geq y \geq z$ . Prove that,


\[\frac{a^2x^2}{(by+cz)(bz+cy)} + \frac{b^2y^2}{(cz+ax)(cx+az)} + \frac{c^2z^2}{(ax+by)(ay+bx)} \geq \frac{3}{4}\]
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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