2005 IMO Problems/Problem 3

Problem

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

Solution

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See Also

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