2. If $x y=a, x z=b, y z=c$, and none of them are equal to 0, then, $x^{2}+y^{2}+z^{2}=$
2. $\frac{(a b)^{2}+(a c)^{2}+(b c)^{2}}{a b c}$.

From the known three equations, multiplying both sides, we get $x y z= \pm \sqrt{a b c}$.
Dividing (*) by the known three equations respectively, we get
$$
\begin{array}{l}
x= \pm \sqrt{\frac{b c}{a}}, y= \pm \sqrt{\frac{a c}{b}}, z= \pm \sqrt{\frac{a b}{c}} . \\
\therefore x^{2}+y^{2}+z^{2} \\
=\left( \pm \sqrt{\frac{b c}{a}}\right)^{2}+\left( \pm \sqrt{\frac{a c}{b}}\right)^{2}+\left( \pm \sqrt{\frac{a b}{c}}\right)^{2} \\
=\frac{a b}{c}+\frac{a c}{b}+\frac{b c}{a}=\frac{(a b)^{2}+(a c)^{2}+(b c)^{2}}{a b c} .
\end{array}
$$