Question 17
Determine all real numbers $x, y, z \in (0,1)$ that satisfy simultaneously the conditions:
$$
\begin{cases}
(x^2 + y^2)\sqrt{1-z^2} \geq z \\
(y^2 + z^2)\sqrt{1-x^2} \geq x \\
(z^2 + x^2)\sqrt{1-y^2} \geq y
\end{cases}
$$
$$
\begin{cases}
(x^2 + y^2)\sqrt{1-z^2} \geq z \\
(y^2 + z^2)\sqrt{1-x^2} \geq x \\
(z^2 + x^2)\sqrt{1-y^2} \geq y
\end{cases}
$$