$\left\{\begin{matrix}x_1-x_2=3\\x_1^3-x_2^3=9\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}(x_1+x_2)^2-4x_1x_2=9\\ [(x_1+x_2)^2-4x_1x_2][(x_1+x_2)^2-x_1x_2]^2=81\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}(x_1+x_2)^2-4x_1x_2=9\\(x_1+x_2)^2-x_1x_2=3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}-3x_1x_2=6\\(x_1+x_2)^2-x_1x_2=3\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}x_1x_2=-2\\x_1+x_2=1\end{matrix}\right.\\ \Leftrightarrow \left\{\begin{matrix}a=-1\\b=-3\end{matrix}\right.$
