IMO 2021, Problem 2
Posted: 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 $x_1, \ldots, x_n.$
\[\sum_{i=1}^{n} \sum_{j=1}^{n} (\sqrt{|x_{i} - x_{j}|}) \leq \sum_{i=1}^{n} \sum_{j=1}^{n} (\sqrt{|x_{i} +x_{j}|})\]
holds for all real numbers $x_1, \ldots, x_n.$