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x^4 + 2z^3 - y =\sqrt3 - 1/4 , y^4 + 2y^3 - x = - \sqrt3 - 1/4

Source: 2010 Saudi Arabia Pre-TST 4.4

December 28, 2021

system of equationsSystemalgebra

Problem Statement

Find all pairs

(x, y)

of real numbers that satisfy the system of equations

\begin{cases} x^4 + 2z^3 - y =\sqrt3 - \dfrac14 \\ y^4 + 2y^3 - x = - \sqrt3 - \dfrac14 \end{cases}