Question 17
Determine all triples $(x, y, z)$ of real numbers that satisfy
$$
\begin{align*}
x + y - z &= -1 \\
x^2 - y^2 + z^2 &= 1 \\
-x^3 + y^3 + z^3 &= -1.
\end{align*}
$$
$$
\begin{align*}
x + y - z &= -1 \\
x^2 - y^2 + z^2 &= 1 \\
-x^3 + y^3 + z^3 &= -1.
\end{align*}
$$