2005 IMO Problems/Problem 3

Problem

Let $x, y, z > 0$ satisfy $xyz\ge 1$ . Prove that $\frac{x^5-x^2}{x^5+y^2+z^2} + \frac{y^5-y^2}{x^2+y^5+z^2} + \frac{z^5-z^2}{x^2+y^2+z^5} \ge 0.$

This problem needs a solution. If you have a solution for it, please help us out by adding it.

2005 IMO (Problems) • Resources
Preceded by Problem 2	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 4
All IMO Problems and Solutions