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System of equations in real numbers

Source: 2018 Latvia BW TST P2

June 4, 2022

algebrasystem of equationsalgebra unsolved

Problem Statement

Find all ordered pairs

(x,y)

of real numbers that satisfy the following system of equations:

\begin{cases} y(x+y)^2=2\\ 8y(x^3-y^3) = 13. \end{cases}