nice inequality
Source: Ireland 1998
July 4, 2009
inequalitiesinequalities proposed
Problem Statement
Prove that if are positive real numbers, then:
\frac{9}{a\plus{}b\plus{}c} \le 2 \left( \frac{1}{a\plus{}b}\plus{}\frac{1}{b\plus{}c}\plus{}\frac{1}{c\plus{}a} \right) \le \frac{1}{a}\plus{}\frac{1}{b}\plus{}\frac{1}{c}.