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(x + y)(y + z)(z + x)/{xyz} if (x+ y}/z=(y + z)/x=(z + x)/y

Source: 2023 Austrian Mathematical Olympiad, Junior Regional Competition , Problem 1

March 26, 2024
algebra

Problem Statement

Let x,y,zx, y, z be nonzero real numbers with x+yz=y+zx=z+xy.\frac{x + y}{z}=\frac{y + z}{x}=\frac{z + x}{y}. Determine all possible values of (x+y)(y+z)(z+x)xyz.\frac{(x + y)(y + z)(z + x)}{xyz}.
(Walther Janous)
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