Possible Duplicate:
Cauchy-Schwarz inequality and three-letter identities (exercise 1.4 from “The Cauchy-Schwarz Master Class”)
Is it true for all $x, y, z > 0$ that
$ x + y + z \leq 2 \left\{ \frac{x^2}{y+z} + \frac{y^2}{x+z} + \frac{z^2}{x+y} \right\} $
This is an exercise (1.4) in "The Cauchy-Schwarz Master Class: An Introduction to the Art of mathematical Inequalities"
The solution suggests applying C-S to $ x + y + z = \frac{x}{\sqrt{y+z}}\sqrt{y+z} + \frac{y}{\sqrt{x+z}}\sqrt{x+z} + \frac{z}{\sqrt{x+y}}\sqrt{x+y} $