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ab / (c+ab) symmetric

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

December 11, 2004
inequalitiesinequalities unsolved

Problem Statement

Let the sum of positive reals a,b,ca,b,c be equal to 1. Prove an inequality abc+ab+bca+bc+acb+ac≤3/2 \sqrt{{ab}\over {c+ab}}+\sqrt{{bc}\over {a+bc}}+\sqrt{{ac}\over {b+ac}}\le 3/2 . proposed by Fedor Petrov
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