IMO 2021, Problem 2

Discussion on International Mathematical Olympiad (IMO)
tanmoy
Posts:312
Joined:Fri Oct 18, 2013 11:56 pm
Location:Rangpur,Bangladesh
IMO 2021, Problem 2

Unread post by tanmoy » Wed Jul 21, 2021 8:11 pm

Show that the inequality
\[\sum_{i=1}^{n} \sum_{j=1}^{n} (\sqrt{|x_{i} - x_{j}|}) \leq \sum_{i=1}^{n} \sum_{j=1}^{n} (\sqrt{|x_{i} +x_{j}|})\]
holds for all real numbers $x_1, \ldots, x_n.$
"Questions we can't answer are far better than answers we can't question"

Post Reply