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(a+b+c+3)/4 is bigger than sum of fractions

Source: European Mathematical Cup, 2015, Senior, P2

December 30, 2016
inequalitiesalgebra

Problem Statement

Let a,b,ca,b,c be positive real numbers such that abc=1abc=1. Prove that a+b+c+34⩾1a+b+1b+c+1c+a.\frac{a+b+c+3}{4}\geqslant \frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}.
Dimitar Trenevski
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