Exponential inequality
Source: Romanian District Olympiad 2006, Grade 10, Problem 1
March 11, 2006
inequalitieslogarithmsinequalities proposed
Problem Statement
Let and x,y,z\in (0, \plus{} \infty) be six real numbers such that
a^x \equal{} bc , b^y \equal{} ca , c^z \equal{} ab .
Prove that
\frac 1{2 \plus{} x} \plus{} \frac 1{2 \plus{} y} \plus{} \frac 1{2 \plus{} z} \leq \frac 34 .
Cezar Lupu