3. Solve the equation $2021 \cdot \sqrt[202]{x^{2020}}-1=2020 x$ for $x \geq 0 \cdot$ (10 points)
Solution. Transform the equation to the form:

$$
\begin{aligned}
& \frac{2020 x+1}{2021}=\sqrt[202]{x^{2020}}, \text { from which } \\
& x+x+\ldots+x+1 \\
& \frac{(2020 \text { instances) }}{2021}=\sqrt[202]{x^{2020}}
\end{aligned}
$$

But by the relation for the arithmetic mean and the geometric mean

![](https://cdn.mathpix.com/cropped/2024_05_06_66ff5449eae3e24affe1g-24.jpg?height=128&width=1518&top_left_y=907&top_left_x=406)

the solution to the equation is $x=1$.

Answer. $x=1$.