Question 149
Find all pairs $(x, y)$ of real numbers that satisfy the system of equations
$$
\begin{cases}
x^{4} + 2x^{3} - y = \sqrt{3} - \dfrac{1}{4} \\
y^{4} + 2y^{3} - x = -\sqrt{3} - \dfrac{1}{4}
\end{cases}
$$
$$
\begin{cases}
x^{4} + 2x^{3} - y = \sqrt{3} - \dfrac{1}{4} \\
y^{4} + 2y^{3} - x = -\sqrt{3} - \dfrac{1}{4}
\end{cases}
$$