MathDB

5

Part of 2015 Dutch Mathematical Olympiad

Problems(1)

|a - b| >= |c| , |b - c| >= |a| and |c - a| >= |b| => one is sum of other two

Source: Dutch NMO 2015 p5

9/7/2019
Given are (not necessarily positive) real numbers a,ba, b, and cc for which ∣a−b∣≥∣c∣,∣b−c∣≥∣a∣|a - b| \ge |c| , |b - c| \ge |a| and ∣c−a∣≥∣b∣|c - a| \ge |b| . Prove that one of the numbers a,ba, b, and cc is the sum of the other two.
algebrainequalities