Question 177
Let $k \in [0, 1]$. Solve the system
$$
\begin{aligned}
k - x^2 &= y, \\
k - y^2 &= z, \\
k - z^2 &= u, \\
k - u^2 &= x
\end{aligned}
$$
in real numbers.
$$
\begin{aligned}
k - x^2 &= y, \\
k - y^2 &= z, \\
k - z^2 &= u, \\
k - u^2 &= x
\end{aligned}
$$
in real numbers.