3

Part of 2004 Bosnia and Herzegovina Team Selection Test

Problems(1)

Bosnia and Herzegovina TST 2004 Day 1 Problem 3

Source: Bosnia and Herzegovina Team Selection Test 2004

a

b

c

be positive real numbers such that

abc=1

. Prove the inequality:

\frac{ab}{a^5+b^5+ab} +\frac{bc}{b^5+c^5+bc}+\frac{ac}{c^5+a^5+ac}\leq 1

Inequalitypositive realalgebrainequalities