Question 71
Do there exist real numbers $x$, $y$, $z$, $t$ that meet the following system of equations?
$$
\begin{cases}
1 + x^3 + y^2 = 0 \\
1 + y^3 + z^2 = 0 \\
1 + z^3 + t^2 = 0 \\
1 + t^3 + x^2 = 0 \\
x + y + z + t = 0
\end{cases}
$$
$$
\begin{cases}
1 + x^3 + y^2 = 0 \\
1 + y^3 + z^2 = 0 \\
1 + z^3 + t^2 = 0 \\
1 + t^3 + x^2 = 0 \\
x + y + z + t = 0
\end{cases}
$$