MathDB

056

Part of 1965 All Russian Mathematical Olympiad

Problems(1)

ASU 056 All Russian MO 1965 min sum of products of x_1,x_2,...,x_n

Source:

6/19/2019
a) Each of the numbers x1,x2,...,xnx_1,x_2,...,x_n can be 1,01, 0, or −1-1. What is the minimal possible value of the sum of all products of couples of those numbers.
b) Each absolute value of the numbers x1,x2,...,xnx_1,x_2,...,x_n doesn't exceed 11. What is the minimal possible value of the sum of all products of couples of those numbers.
algebraminimuminequalities