Very easy inequality
Source: JBMO Shortlist 2002
November 12, 2008
inequalitiesvectorinductioninequalities proposed
Problem Statement
Let be positive real numbers. Prove the inequality:
\frac {a^3}{b^2} \plus{} \frac {b^3}{c^2} \plus{} \frac {c^3}{a^2}\ge \frac {a^2}{b} \plus{} \frac {b^2}{c} \plus{} \frac {c^2}{a}