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An integer is the arithmetic mean of the others

Source: Romanian DMO, 8th grade, problem 1

March 23, 2007
algebra proposedalgebra

Problem Statement

Three positive reals x,y,zx,y,z are given so that xy=z−x+1y=z+12.xy=\frac{z-x+1}{y}=\frac{z+1}2. Prove that one of the numbers is the arithmetic mean of the other two.
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