Problem

Source: Iran Third Round 1997, E1, P1

Tags: inequalities, inequalities proposed



Let $a,b,c,d$ be positive real numbers. Prove that \[\frac{a}{b+2c+3d}+\frac{b}{c+2d+3a}+\frac{c}{d+2a+3b}+\frac{d}{a+2b+3c} \geq \frac{2}{3}.\]