MathDB
Omogeneus inequality by Daij Grinberg

Source: Oliforum contest 2009, round 2/4

October 18, 2009
inequalitiesinequalities proposed

Problem Statement

Let a,b,c a,b,c be positive reals; show that \displaystyle a \plus{} b \plus{} c \leq \frac {bc}{b \plus{} c} \plus{} \frac {ca}{c \plus{} a} \plus{} \frac {ab}{a \plus{} b} \plus{} \frac {1}{2}\left(\frac {bc}{a} \plus{} \frac {ca}{b} \plus{} \frac {ab}{c}\right) (Darij Grinberg)