CN-SMO 2009 Problem 3

Let $x,y,z$ be positive reals such that $\sqrt{a}=x(y-z)^2$ , $\sqrt{b}=y(z-x)^2$ and $\sqrt{c}=z(x-y)^2$ . Prove that $$a^2+b^2+c^2 \geq 2(ab+bc+ca)$$