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RU-ALLRUSSIAN 1979 Problem 8

    a and b are real numbers. Find real x and y satisfying: (x−y(x2−y2)1/2=a(1−x2+y2)1/2(\mathrm{x} - \mathrm{y}(\mathrm{x}^2 - \mathrm{y}^2)^{1 / 2} = \mathrm{a}(1 - \mathrm{x}^2 + \mathrm{y}^2)^{1 / 2} and (y−x(x2−y2)1/2=b(1−x2+y2)1/2(\mathrm{y} - \mathrm{x}(\mathrm{x}^2 - \mathrm{y}^2)^{1 / 2} = \mathrm{b}(1 - \mathrm{x}^2 + \mathrm{y}^2)^{1 / 2} .

    Dataset text NuminaMath olympiads. Quoted with source.

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