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Bosnia and Herzegovina TST 2004 Day 1 Problem 3

Source: Bosnia and Herzegovina Team Selection Test 2004

September 17, 2018
Inequalitypositive realalgebrainequalities

Problem Statement

Let aa, bb and cc be positive real numbers such that abc=1abc=1. Prove the inequality: aba5+b5+ab+bcb5+c5+bc+acc5+a5+ac≤1\frac{ab}{a^5+b^5+ab} +\frac{bc}{b^5+c^5+bc}+\frac{ac}{c^5+a^5+ac}\leq 1
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