SE-SKOLORNAS 1988 Problem 3

Show that if $x_1+x_2+x_3 = 0$ for real numbers $x_1,x_2,x_3$ , then $x_1x_2+x_2x_3+x_3x_1\le 0$ .

Find all $n \ge 4$ for which $x_1+x_2+...+x_n = 0$ implies $x_1x_2+x_2x_3+...+x_{n-1}x_n+x_nx_1 \le 0$ .