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2021 IMO Problems/Problem 2

Revision as of 23:04, 5 June 2023 by Mathhyhyhy (talk | contribs) (→‎Video solutions)

Problem

Show that the inequality \[\sum_{i=1}^n \sum_{j=1}^n \sqrt{|x_i-x_j|} \le \sum_{i=1}^n \sum_{j=1}^n \sqrt{|x_i+x_j|}\] holds for all real numbers $x_1,x_2,\dots,x_n$.

Solution

Video solutions

https://youtu.be/cI9p-Z4-Sc8 [Video contains solutions to all day 1 problems]

https://youtu.be/akJOPrh5sqg [uses integral]

https://www.youtube.com/watch?v=P9Ge8HAf6xk

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