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Russia Inequality

Source:

December 19, 2003
inequalities

Problem Statement

(Russia 1195) If x, y > 0, prove that

x/(x^4 + y^2) + y/(y^4 + x^2) <= 1/(xy)

Thoughts?

By the way, this was in Kiran Kedlaya's MOP notes and said to be from Russia 1995, but John Scholes' Kalva archive doesn't have this problem under Russia 1995. Odd.

Hint:

This was in the Power Mean Inequality section in the lecture notes.
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