Problem

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Tags: algebra, inequalities



Let $t_{k} = a_{1}^k + a_{2}^k +...+a_{n}^k$, where $a_{1}$, $a_{2}$, ... $a_{n}$ are positive real numbers and $k \in \mathbb{N}$. Prove that $$\frac{t_{5}^2 t_1^{6}}{15} - \frac{t_{4}^4 t_{2}^2 t_{1}^2}{6} + \frac{t_{2}^3 t_{4}^5}{10} \geq 0 $$ Proposed by Daniel Velinov