KöMaL 2013 B4520

Given the positive numbers $a$, $b$ and $c$, determine the values of the non-negative variables $x$, $y$, $z$ such that the expression $a^2\frac{x}{y+z} + b^2\frac{y}{z+x} + c^2\frac{z}{x+y}$ is a minimum.