12.3 Given that $x-\frac{1}{x}=2 b$ and $x^{3}-\frac{1}{x^{3}}=c$, find the value of $c$.
Reference: 1990 FI2.2
$$
\begin{array}{l}
x-\frac{1}{x}=3 \Rightarrow x^{2}-2+\frac{1}{x^{2}}=9 \Rightarrow x^{2}+\frac{1}{x^{2}}=11 \\
c=x^{3}-\frac{1}{x^{3}}=\left(x-\frac{1}{x}\right)\left(x^{2}+1+\frac{1}{x^{2}}\right)=3 \times(11+1)=36
\end{array}
$$