36. Given that $x, y, z$ are positive numbers, find the minimum value of the following two expressions:
(1) $\frac{x^{2}+y^{2}+z^{2}}{x y+y z}$; $\frac{x^{2}+y^{2}+2 z^{2}}{x y+y z}$. (2008 Croatian Mathematical Olympiad)
36. (1) By the AM-GM inequality, $\frac{x^{2}+y^{2}+z^{2}}{x y+y z}=\frac{x^{2}+\frac{1}{2} y^{2}+\frac{1}{2} y^{2}+z^{2}}{x y+y z} \geqslant$ $\frac{\sqrt{2} x y+\sqrt{2} y z}{x y+y z}=\sqrt{2}$.
(2) $\frac{x^{2}+y^{2}+2 z^{2}}{x y+y z}=\frac{x^{2}+\frac{2}{3} y^{2}+\frac{1}{3} y^{2}+2 z^{2}}{x y+y z} \geqslant \frac{\sqrt{\frac{8}{3}} x y+\sqrt{\frac{8}{3}} y z}{x y+y z}=\frac{2 \sqrt{6}}{3}$.