Question 3
(CZS 4) Let $x_1,x_2,\ldots,x_n$ be real numbers satisfying $x_1+x_2+\cdots+x_n=0$. Let $m$ be the least and $M$ the greatest among them. Prove that
$$x_1^2+x_2^2+\cdots+x_n^2\le-nmM.$$
$$x_1^2+x_2^2+\cdots+x_n^2\le-nmM.$$
IMO 1972 — Shortlisted problems Question 3
IMO Shortlist · IMO 1972 — Shortlisted problems