Hard inequality
Source: Serbian National Olympiad 2008
April 13, 2008
inequalitiesfunctionCauchy Inequalityinequalities unsolved
Problem Statement
Let , , be positive real numbers such that a \plus{} b \plus{} c \equal{} 1. Prove inequality:
\frac{1}{bc \plus{} a \plus{} \frac{1}{a}} \plus{} \frac{1}{ac \plus{} b \plus{} \frac{1}{b}} \plus{} \frac{1}{ab \plus{} c \plus{} \frac{1}{c}} \leqslant \frac{27}{31}.