Petru Morosan - Trident Problema 3

[emiemiemi]

Fie $n \in \mathbb{N}, n \ge 2$. Aratati ca:
$\displaystyle \frac{x_1^n+x_2^n+...+x_n^n}{x_1x_2 \cdot ... \cdot x_n}+\frac{\sqrt[n]{x_1x_2 \cdot ... \cdot x_n}}{x_1+x_2+...+x_n} \ge n+\frac{1}{n}$,$\forall x_1,x_2,...,x_n \in (0, \infty )$.

[Marius Stănean]

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