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Irish Mathematical Olympiad 2014 (1)

Source: Paper 1 , Problem 4

September 6, 2014
algebra proposedalgebra

Problem Statement

Three different non-zero real numbers a,b,ca,b,c satisfy the equations a+2b=b+2c=c+2a=pa+\frac{2}{b}=b+\frac{2}{c}=c+\frac{2}{a}=p , where pp is a real number. Prove that abc+2p=0.abc+2p=0.
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