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Source: Romania District Olympiad 2014,grade VII(problem 2)

March 8, 2014
inequalitiesinequalities proposedalgebra

Problem Statement

Let real numbers a,b,ca,b,c such that ∣a−b∣≥∣c∣,∣b−c∣≥∣a∣,∣c−a∣≥∣b∣.\left| a-b \right|\ge \left| c \right|,\left| b-c \right|\ge \left| a \right|,\left| c-a \right|\ge \left| b \right|. Prove that a=b+ca=b+c or b=c+ab=c+a or c=a+b.c=a+b.
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