3

Part of 1972 IMO Shortlist

Problems(1)

Source: New Ineq

The least number is

m

and the greatest number is

M

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

InequalityoptimizationmaximizationIMO ShortlistIMO Shortlist 1972