MathDB

225

Part of 1976 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 225 All Soviet Union MO 1976 |a|+|b|+|c|+|d| \ge |a+d|+|b+d|+|c+d|

Source:

7/5/2019
Given 44 vectors a,b,c,da,b,c,d in the plane, such that a+b+c+d=0a+b+c+d=0. Prove the following inequality: ∣a∣+∣b∣+∣c∣+∣d∣≥∣a+d∣+∣b+d∣+∣c+d∣|a|+|b|+|c|+|d| \ge |a+d|+|b+d|+|c+d|
inequalitiesvectoralgebra