Difference between revisions of "2011 OIM Problems/Problem 5"
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== Problem == | == Problem == | ||
− | Let <math>x_1, \cdots , x_n</math> be positive real numbers. Prove that there exist <math> | + | Let <math>x_1, \cdots , x_n</math> be positive real numbers. Prove that there exist <math>a_1, \cdots , a_n \in \left\{ -1, 1 \right\}</math> such that |
<cmath>a_1x_1^2+\cdots+a_nx_n^2\ge (a_1x_1+\cdots+a_nx_n)^2</cmath> | <cmath>a_1x_1^2+\cdots+a_nx_n^2\ge (a_1x_1+\cdots+a_nx_n)^2</cmath> |
Latest revision as of 16:00, 14 December 2023
Problem
Let be positive real numbers. Prove that there exist
such that
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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