IMO 2005 Problem 3

Let $x,y,z$ be three positive reals such that $xyz\geq 1$ . Prove that $$\frac { x^5-x^2 }{x^5+y^2+z^2} + \frac {y^5-y^2}{x^2+y^5+z^2} + \frac {z^5-z^2}{x^2+y^2+z^5} \geq 0 .$$ Hojoo Lee, Korea