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x^2 + y^2 = 2, \frac{x^2}{2 - y}+\frac{y^2}{2 - x}= 2

Source: 2022 NZMO - New Zealand Maths Olympiad Round 1 p3

October 9, 2022

algebrasystem of equations

Problem Statement

Find all real numbers

x

and

y

such that

x^2 + y^2 = 2

\frac{x^2}{2 - y}+\frac{y^2}{2 - x}= 2.