(a/(1 + ab))^2 + (b/(1 + bc))^2 + (c/(1 + ca))^2 ≥ 3/4
Source: Spain National Olympiad (OME) 2009, Problem 4
December 29, 2009
inequalitiesinequalities proposed
Problem Statement
Let, real positive numbers with abc \equal{} 1
Prove:
(\frac {a}{1 \plus{} ab})^2 \plus{} (\frac {b}{1 \plus{} bc})^2 \plus{} (\frac {c}{1 \plus{} ca})^2\geq \frac {3}{4}
Thanks!