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x - 1/y^2 = y - 1/z^2 = z - /x^2

Source: 2011 Swedish Mathematical Competition p3

April 30, 2021

system of equationsSystemalgebra

Problem Statement

Find all positive real numbers

x, y, z

, such that

x - \frac{1}{y^2} = y - \frac{1}{z^2}= z - \frac{1}{x^2}