3. Solve the equation $\left(101 x^{2}-18 x+1\right)^{2}-121 x^{2} \cdot\left(101 x^{2}-18 x+1\right)+2020 x^{4}=0$ Answer: $\frac{1}{9}, \frac{1}{18}$
Solution. Let $y=\left(101 x^{2}-18 x+1\right), z=\frac{y}{x^{2}}$. After dividing the equation by (non-zero number: $\mathrm{x}=0$ is not suitable) $x^{4}$, we get $z^{2}-121 z+2020=0$. The roots of this equation can be easily found using Vieta's theorem: $\mathrm{z}=101$ or $\mathrm{z}=20$. In the first case, we get the equation $-18 x+1=0$, and in the second case, $-81 x^{2}-$ $18 x+1=0$, from which we find the desired solution.

Evaluation. Full solution - 7 points.