Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2021 IMO Problems/Problem 2

Revision as of 09:33, 27 July 2021 by Ftheftics (talk | contribs) (→‎Video solution)

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 with Integral

https://youtu.be/akJOPrh5sqg

Video solution

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2021_IMO_Problems/Problem_2&oldid=159201"