IMO 1972 LL NET25

Origin: NET

Problem

We consider n real variables xi (1 \leqi \leqn), where n is an integer and n \geq2. The product of these variables will be denoted by p, their sum by s, and the sum of their squares by S. Furthermore, let \alpha be a positive constant. We now study the inequality ps \leqS\alpha. Prove that it holds for every n-tuple (xi) if and only if \alpha = n+1 2 .