Question 41
For real numbers $-1 \lt x_1, x_2, \dots, x_n \lt 1$ with sum $x_1 + x_2 + \dots + x_n = 0$, prove that we have
$$
\sum_{i=1}^{n} \sum_{j=1}^{n} x_i x_j \sqrt{1 - x_i^2 x_j^2} \le 0
$$
and determine the conditions under which equality holds.
$$
\sum_{i=1}^{n} \sum_{j=1}^{n} x_i x_j \sqrt{1 - x_i^2 x_j^2} \le 0
$$
and determine the conditions under which equality holds.