Question 51
Given an integer $n \ge 3$. Consider $n$ real numbers $x_1, x_2, \dots, x_n$ satisfying at the same time the following conditions:
i/ $x_1 \ge x_2 \ge \dots \ge x_n$;
ii/ $\sum_{i=1}^{n} x_i = 0$;
iii/ $\sum_{i=1}^{n} x_i^2 = n(n-1)$.
Find the maximum and the minimum values of the sum $S = x_1 + x_2$.
i/ $x_1 \ge x_2 \ge \dots \ge x_n$;
ii/ $\sum_{i=1}^{n} x_i = 0$;
iii/ $\sum_{i=1}^{n} x_i^2 = n(n-1)$.
Find the maximum and the minimum values of the sum $S = x_1 + x_2$.