Strange condition, easy inequality
Source: Serbian JBTST 4, Day 2
May 31, 2009
inequalitiesinequalities proposed
Problem Statement
For positive real numbers the inequality
\frac1{x^2\plus{}1}\plus{}\frac1{y^2\plus{}1}\plus{}\frac1{z^2\plus{}1}\equal{}\frac12
holds. Prove the inequality
\frac1{x^3\plus{}2}\plus{}\frac1{y^3\plus{}2}\plus{}\frac1{z^3\plus{}2}<\frac13.