Question 44
Determine all real solutions $(x, y, z)$ of the system
$$
\frac{4 x^{2}}{1+4 x^{2}}=y, \quad \frac{4 y^{2}}{1+4 y^{2}}=z, \quad \frac{4 z^{2}}{1+4 z^{2}}=x
$$
$$
\frac{4 x^{2}}{1+4 x^{2}}=y, \quad \frac{4 y^{2}}{1+4 y^{2}}=z, \quad \frac{4 z^{2}}{1+4 z^{2}}=x
$$