数学

优雅不等式

设$x_1,x_2,\cdots,x_n$为实数。证明：

$\large{~\left(\sum_{1\leq~i\lt~j\leq~n}|x_i-x_j|\right)^2~\geq~\sum_{1\leq~i\lt~j\leq~n}|x_i-x_j|^2}$