When Squares Beat the Sum

Problem

Let $x_1, \dots, x_n$ ( $n \ge 2$ ) be positive reals with $x_1x_2\cdots x_n > 1$ . Prove that

x_1^2 + x_2^2 + \cdots + x_n^2 > x_1 + x_2 + \cdots + x_n.

Answer

Solution

Difficulty	7/10
Topics	AM-GM, inequality

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