One, (20 points) Given real numbers $x, y, z$ satisfy
$$
\begin{array}{l}
\bar{x}-y=\frac{x}{y+z}, \\
z^{2}=x(y+z)-y(x-y) .
\end{array}
$$

Find the value of $\frac{y^{2}+z^{2}-x^{2}}{2 y z}$.
$$
\begin{array}{l}
\text { From equation (1), we get } y^{2}-x^{2}=-y(x+z). \\
\text { From equation (2), we get } z^{2}=x z+y^{2}. \\
\text { Then } \frac{y^{2}+z^{2}-x^{2}}{2 y z}=\frac{z^{2}-y(x+z)}{2 y z} \\
=\frac{x z+y^{2}-y(x+z)}{2 y z} \\
=\frac{1}{2} \cdot \frac{x-y}{y} \cdot \frac{z-y}{z} \\
=\frac{1}{2} \cdot \frac{y+z}{x} \cdot \frac{z-y}{z} \\
=\frac{1}{2} \cdot \frac{z^{2}-y^{2}}{x z}=\frac{1}{2} . \\
\end{array}
$$