9.1. Solve the equation:

$$
\left(x^{2}-20\right)^{2}+\left(x^{2}-19\right)^{2}=2019
$$
Solution. Let $x^{2}-20=y$; then $y^{2}+y-1009=0(D=4037)$ and $y=\frac{-1 \pm \sqrt{4037}}{2}$. For the smaller root, the reverse substitution leads to the condition $x^{2}<0$ (no solutions), the larger root gives Answer: $x= \pm \sqrt{\frac{39+\sqrt{4037}}{2}}$.