Inequality from JMO 2010
Source: 2010 Japan Mathematical Olympiad Finals, Problem 4
February 11, 2010
inequalitiesinequalities proposed
Problem Statement
Let be positive real numbers.
Prove that
\frac {1 \plus{} yz \plus{} zx}{(1 \plus{} x \plus{} y)^2} \plus{} \frac {1 \plus{} zx \plus{} xy}{(1 \plus{} y \plus{} z)^2} \plus{} \frac {1 \plus{} xy \plus{} yz}{(1 \plus{} z \plus{} x)^2}\geq 1