MathNet 2014 Question 95

Let $n$ be a positive integer and $x_1,\ldots,x_n$ positive real numbers. Prove there exist $a_1,\ldots,a_n\in\{-1,1\}$ such that $$a_1x_1^2+\cdots+a_nx_n^2\ge(a_1x_1+\cdots+a_nx_n)^2.$$