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\frac{x+y}{x^2 +y^2} = a , \frac{x^3 +y^3}{x^2 +y^2} = b

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1999 p6

February 20, 2020
algebrasystem of equations

Problem Statement

Find all pairs of real numbers a,ba,b for which the system of equations {x+yx2+y2=ax3+y3x2+y2=b \begin{cases} \dfrac{x+y}{x^2 +y^2} = a \\ \\ \dfrac{x^3 +y^3}{x^2 +y^2} = b \end{cases} has a real solution.
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