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2003 USAMO Problems/Problem 5

Revision as of 16:53, 20 August 2008 by Minsoens (talk | contribs) (New page: == Problem == Let <math>a</math>, <math>b</math>, <math>c</math> be positive real numbers. Prove that <center><math>\dfrac{(2a + b + c)^2}{2a^2 + (b + c)^2} + \dfrac{(2b + c + a)^2}{2b^2 ...)

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Problem

Let $a$ , $b$ , $c$ be positive real numbers. Prove that

$\dfrac{(2a + b + c)^2}{2a^2 + (b + c)^2} + \dfrac{(2b + c + a)^2}{2b^2 + (c + a)^2} + \dfrac{(2c + a + b)^2}{2c^2 + (a + b)^2} \le 8.$

Solution

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