Question 65
Find all quadruples $(a, b, c, d)$ of real numbers that simultaneously satisfy the following equations:
$$
\begin{cases} a^3 + c^3 = 2 \\ a^2b + c^2d = 0 \\ b^3 + d^3 = 1 \\ ab^2 + cd^2 = -6. \end{cases}
$$
$$
\begin{cases} a^3 + c^3 = 2 \\ a^2b + c^2d = 0 \\ b^3 + d^3 = 1 \\ ab^2 + cd^2 = -6. \end{cases}
$$