Question 3
Let $n\ge3$ be an integer and let $x_1,\ldots,x_n$ be real numbers such that
$$\sum_{i=1}^n x_i=0,\qquad \sum_{i=1}^n x_i^2=n(n-1),\qquad x_1\ge x_2\ge\cdots\ge x_n.$$
Find the maximum and minimum of $f=x_1+x_2$.
$$\sum_{i=1}^n x_i=0,\qquad \sum_{i=1}^n x_i^2=n(n-1),\qquad x_1\ge x_2\ge\cdots\ge x_n.$$
Find the maximum and minimum of $f=x_1+x_2$.