MathDB

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

Source: Dutch NMO 2015 p5

September 7, 2019

algebrainequalities

Problem Statement

Given are (not necessarily positive) real numbers

a, b

, and

c

for which

|a - b| \ge |c| , |b - c| \ge |a|

and

|c - a| \ge |b|

. Prove that one of the numbers

a, b

, and

c

is the sum of the other two.