Question 71
Suppose $x_1, x_2, \dots, x_n$ are complex numbers. Prove that
$$
\sum_{i,j=1}^{n} |x_i - x_j|^2 \le \sum_{i,j=1}^{n} |x_i + x_j|^2,
$$
with equality iff $x_1 + x_2 + \dots + x_n = 0$.
$$
\sum_{i,j=1}^{n} |x_i - x_j|^2 \le \sum_{i,j=1}^{n} |x_i + x_j|^2,
$$
with equality iff $x_1 + x_2 + \dots + x_n = 0$.