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

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

But by the inequality between the arithmetic mean and the geometric mean

![](https://cdn.mathpix.com/cropped/2024_05_06_66ff5449eae3e24affe1g-49.jpg?height=124&width=1454&top_left_y=907&top_left_x=423)
the solution to the equation is $x=1$.

Answer: $x=1$.