Question 158
Determine the largest real number $C$ such that
$$
\sum_{i=1}^{n} \sum_{j=1}^{n} (n - |i - j|) x_i x_j \ge C \sum_{i=1}^{n} x_i^2
$$
holds for every positive integer $n$ and any real numbers $x_1, x_2, \dots, x_n$.
$$
\sum_{i=1}^{n} \sum_{j=1}^{n} (n - |i - j|) x_i x_j \ge C \sum_{i=1}^{n} x_i^2
$$
holds for every positive integer $n$ and any real numbers $x_1, x_2, \dots, x_n$.