This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 2

1972 IMO Shortlist, 3
Tags: Inequality , optimization , maximization , IMO Shortlist , IMO Shortlist 1972
The least number is $m$ and the greatest number is $M$ among $ a_1 ,a_2 ,\ldots,a_n$ satisfying $ a_1 \plus{}a_2 \plus{}...\plus{}a_n \equal{}0$. Prove that \[ a_1^2 \plus{}\cdots \plus{}a_n^2 \le\minus{}nmM\]

1972 IMO Longlists, 11
Tags: Inequality , optimization , maximization , IMO Shortlist , IMO Shortlist 1972
The least number is $m$ and the greatest number is $M$ among $ a_1 ,a_2 ,\ldots,a_n$ satisfying $ a_1 \plus{}a_2 \plus{}...\plus{}a_n \equal{}0$. Prove that \[ a_1^2 \plus{}\cdots \plus{}a_n^2 \le\minus{}nmM\]