- #1
Kizaru
- 45
- 0
Homework Statement
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]
Homework Equations
Cauchy-Schwarz and Arithmetic Geometric Mean inequalities.
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.
Last edited: