4

Part of 2004 239 Open Mathematical Olympiad

Problems(1)

ab / (c+ab) symmetric

Source: 239MO 2004, grade 8-9, problem 5, grade 10-11, problem 4

Let the sum of positive reals

a,b,c

be equal to 1. Prove an inequality

\sqrt{{ab}\over {c+ab}}+\sqrt{{bc}\over {a+bc}}+\sqrt{{ac}\over {b+ac}}\le 3/2

. proposed by Fedor Petrov

inequalitiesinequalities unsolved