2011 OIM Problems/Problem 5

Problem

Let $x_1, \cdots , x_n$ be positive real numbers. Prove that there exist $a1, \cdots , a_n \in \left\{−1, 1\right\}$ (Error compiling LaTeX. Unknown error_msg) such that

$a_1x_1^2+\cdots+a_nx_n^2\ge (a_1x_1+\cdots+a_nx_n)^2$

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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2011 OIM Problems/Problem 5

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