Let \(x, y, z\) be three positive reals such that \(xyz \ge 1\). Prove that $$ \frac{x^5\;-\;x^2}{x^5\;+\;y^2\;+\;z^2}\;+\;\frac{y^5\;-\;y^2}{x^2\;+\;y^5\;+\;z^2}\;+\;\frac{z^5\;-\;z^2}{x^2\;+\;y^2\;+\;z^5}\;\geq\;0. $$
| Attributes | Олімпіадна |
|---|---|
| Source | International Mathematical Olympiad |
| Year | 2005 |
| Number | 3 |
| Difficulty | 10.0 |
| Themes |