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Inequality holding for n reals always.

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December 6, 2010
inequalitiesinequalities unsolved

Problem Statement

We consider nn real variables xi(1≤i≤n)x_i(1 \le i \le n), where nn is an integer and n≥2n \ge 2. The product of these variables will be denoted by pp, their sum by ss, and the sum of their squares by SS. Furthermore, let α\alpha be a positive constant. We now study the inequality ps≤Sαps \le S\alpha. Prove that it holds for every nn-tuple (xi)(x_i) if and only if α=n+12\alpha=\frac{n+1}{2}
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