Let
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
be a positive integer and let
![x_1\le x_2\le\cdots\le x_n](/media/m/d/c/4/dc4f117856216c1470a755ad68310882.png)
be real numbers.
Prove that
Show that the equality holds if and only if
![x_1, \ldots, x_n](/media/m/0/7/9/0799442355b568b71d32027391bc4ef9.png)
is an arithmetic sequence.
%V0
Let $n$ be a positive integer and let $x_1\le x_2\le\cdots\le x_n$ be real numbers.
Prove that
$$\left(\sum_{i,j=1}^{n}|x_i-x_j|\right)^2\le\frac{2(n^2-1)}{3}\sum_{i,j=1}^{n}(x_i-x_j)^2.$$
Show that the equality holds if and only if $x_1, \ldots, x_n$ is an arithmetic sequence.