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China South East Mathematical Olympiad 2016 Grade11 Q2

Source: China Nanchang

July 30, 2016

inequalities

Problem Statement

Let

n

be positive integer,

x_1,x_2,\cdots,x_n

be positive real numbers such that

x_1x_2\cdots x_n=1

. Prove that

\sum\limits_{i = 1}^{n}x_i\sqrt{x^2_1+x^2_2+\cdots x^2_i}\ge\frac{n+1}{2}\sqrt{n}