$\begin{align}
& {{({{x}^{2}}-2)}^{2}}-9{{x}^{2}}+32=0\Rightarrow {{({{x}^{2}}-2)}^{2}}-9{{x}^{2}}+18+14=0\Rightarrow {{({{x}^{2}}-2)}^{2}}-9({{x}^{2}}-2)+14=0 \\
& \xrightarrow[{}]{{{x}^{2}}-2=t}{{t}^{2}}-9t+14=0\Rightarrow (t-2)(t-7)=0\Rightarrow \left\{ \begin{matrix}
t=2\Rightarrow {{x}^{2}}-2=2\Rightarrow {{x}^{2}}=4\Rightarrow x=\pm 2 \\
t=7\Rightarrow {{x}^{2}}-2=7\Rightarrow {{x}^{2}}=9\Rightarrow x=\pm 3 \\
\end{matrix} \right. \\
\end{align}$
این معادله چهار ریشهٔ حقیقی دارد.
مهدی خلجی 
