2011 OIM Problems/Problem 5
Problem
Let 
be positive real numbers. Prove that there exist 
such that
![\[a_1x_1^2+\cdots+a_nx_n^2\ge (a_1x_1+\cdots+a_nx_n)^2\]](http://latex.artofproblemsolving.com/f/3/3/f33fbd157011e9f38c438d248986b67de381da06.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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