2021 IMO Problems/Problem 2
Revision as of 00:58, 28 July 2021 by Renrenthehamster (talk | contribs) (Consolidate video solutions under one category)
Problem
Show that the inequality
![\[\sum_{i=1}^n \sum_{j=1}^n \sqrt{|x_i-x_j|} \le \sum_{i=1}^n \sum_{j=1}^n \sqrt{|x_i+x_j|}\]](http://latex.artofproblemsolving.com/6/2/6/6264c77345de1aea2a587da1100b58af528389ae.png)
holds for all real numbers 
.
Video solutions
https://youtu.be/cI9p-Z4-Sc8 [Video contains solutions to all day 1 problems] https://youtu.be/akJOPrh5sqg [uses integral]
