MathDB

a,b,c

Source: Iranian National Olympiad (3rd Round) 2002

October 1, 2006

inequalitiesinequalities proposed

Problem Statement

Let

a,b,c\in\mathbb R^{n}, a+b+c=0

and

\lambda>0

. Prove that

\prod_{cycle}\frac{|a|+|b|+(2\lambda+1)|c|}{|a|+|b|+|c|}\geq(2\lambda+3)^{3}