MathNet 2009-part-01 — 175 problems (EN–VI) Question 136

Let $x$, $y$, $z$ be positive numbers, and $\sqrt{a} = x(y-z)^2$, $\sqrt{b} = y(z-x)^2$, $\sqrt{c} = z(x-y)^2$. Prove that $a^2 + b^2 + c^2 \ge 2(ab + bc + ca)$. (Posed by Tang Lihua)