IR-MO 2002 Problem 1

Let $a,b,c\in\mathbb R^{n}, a+b+c=0$ and $\lambda>0$ . Prove that $\prod_{cycle}\frac{|a|+|b|+(2\lambda+1)|c|}{|a|+|b|+|c|}\geq(2\lambda+3)^{3}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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