Vietnam MO 2008 Inequality
Source: Vietnam MO 2008, Problem 6
August 26, 2008
inequalitiesquadraticsinequalities unsolvedalgebraHigh school olympiadVietnam
Problem Statement
Let be distinct non-negative real numbers. Prove that
\frac{1}{(x\minus{}y)^2} \plus{} \frac{1}{(y\minus{}z)^2} \plus{} \frac{1}{(z\minus{}x)^2} \geq \frac{4}{xy \plus{} yz \plus{} zx}.
When does the equality hold?