4-132 There are three unknowns $x, y, z$ satisfying the following equations
$$
\left\{\begin{array}{l}
x+y+z=a, \\
x^{2}+y^{2}+z^{2}=b^{2}, \\
x^{-1}+y^{-1}+z^{-1}=c^{-1} .
\end{array}\right.
$$

Try to determine the value of $x^{3}+y^{3}+z^{3}$.
[Solution] (1) $)^{2}-$ (2) gives
$$
x y+y z+z x=\frac{1}{2}\left(a^{2}-b^{2}\right) .
$$

From (3) we get $x y z=c(x y+y z+z x)=\frac{c\left(a^{2}-b^{2}\right)}{2}$.
Therefore, $x^{3}+y^{3}+z^{3}$
$$
\begin{array}{l}
=(x+y+z)^{3}-3(x+y+z)(x y+y z+z x)+3 x y z \\
=a^{3}-3 a \cdot \frac{1}{2}\left(a^{2}-b^{2}\right)+3 \cdot \frac{c\left(a^{2}-b^{2}\right)}{2} \\
=a^{3}+\frac{3}{2}\left(a^{2}-b^{2}\right)(c-a) .
\end{array}
$$