FUN WITH EQUATIONS

Your system of equations $\begin{aligned} ax^2 - bx^3 + (2 - b)x &= 7, \\ x^2 (a^2 x^2 + 4ax + 4) &= 9, \\ bx^2 (ax^3 + 2x^2 + ax + 2) &= 8 \end{aligned}$ is inconsistent. If you let $u = ax^2 + 2x$ and $v = bx^3 + bx$ , then your equations become $\begin{aligned} u - v &= 7, \\ u^2 &= 9, \\ uv &= 8. \end{aligned}$ There are no values of $u$ and $v$ that satisfy all three equations.