Difference between revisions of "2021 IMO Problems/Problem 2"

(Video solution)
(Consolidate video solutions under one category)
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holds for all real numbers <math>x_1,x_2,\dots,x_n</math>.
 
holds for all real numbers <math>x_1,x_2,\dots,x_n</math>.
  
==Solution with Integral ==
+
==Video solutions==
https://youtu.be/akJOPrh5sqg
 
 
 
==Video solution==
 
 
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]
 +
https://youtu.be/akJOPrh5sqg [uses integral]

Revision as of 00:58, 28 July 2021

Problem

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

Video solutions

https://youtu.be/cI9p-Z4-Sc8 [Video contains solutions to all day 1 problems] https://youtu.be/akJOPrh5sqg [uses integral]

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