easy
Source: Ireland 1999
July 4, 2009
inequalitiesinequalities proposed
Problem Statement
The sum of positive real numbers is . Prove that:
\frac{a^2}{a\plus{}b}\plus{}\frac{b^2}{b\plus{}c}\plus{}\frac{c^2}{c\plus{}d}\plus{}\frac{d^2}{d\plus{}a} \ge \frac{1}{2},
with equality if and only if a\equal{}b\equal{}c\equal{}d\equal{}\frac{1}{4}.