(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that a, b, c are real numbers and x, y, z >= 0. Prove that

[tex] \frac{a^2}{x} + \frac{b^2}{y} + \frac{c^2}{z} \geq \frac{ (a+b+c)^2}{x+y+z}[/tex]

2. Relevant equations

Cauchy-Schwarz and Arithmetic Geometric Mean inequalities.

3. The attempt at a solution

I wasn't really sure how to approach this problem. I tried brute forcing a solution by multiplying everything out to get common denominators, but that became a mess. I tried a geometric approach of two vectors but didn't get anywhere with it.

Any help would be appreciated. Thanks.

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# Homework Help: Suppose a, b, c are real numbers and x,y,z>=0. Prove the following inequality

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