Difference between revisions of "2021 IMO Problems/Problem 2"
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==Video solutions== | ==Video solutions== | ||
https://youtu.be/cI9p-Z4-Sc8 [Video contains solutions to all day 1 problems] | https://youtu.be/cI9p-Z4-Sc8 [Video contains solutions to all day 1 problems] | ||
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https://youtu.be/akJOPrh5sqg [uses integral] | https://youtu.be/akJOPrh5sqg [uses integral] | ||
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| + | https://www.youtube.com/watch?v=P9Ge8HAf6xk | ||
Revision as of 15:21, 3 August 2021
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]
