Problem

Source: Thailand Mathematical Olympiad 2015 p2

Tags: algebra, inequalities



Let $a, b, c$ be positive reals with $abc = 1$. Prove the inequality $$\frac{a^5}{a^3 + 1}+\frac{b^5}{b^3 + 1}+\frac{c^5}{c^3 + 1} \ge \frac32$$and determine all values of a, b, c for which equality is attained