Task 1. (5 points) Calculate

$$
\left(\frac{10001}{20232023}-\frac{10001}{20222022}\right) \cdot 4090506+\sqrt{4092529}
$$
# Solution.

$$
\begin{aligned}
& \left(\frac{10001}{20232023}-\frac{10001}{20222022}\right) \cdot 4090506+\sqrt{4092529} \\
& =\left(\frac{10001}{2023 \cdot 10001}-\frac{10001}{2022 \cdot 10001}\right) \cdot 4090506+\sqrt{2023^{2}}= \\
& \quad=\left(\frac{1}{2023}-\frac{1}{2022}\right) \cdot 2022 \cdot 2023+2023=\frac{2022-2023}{2022 \cdot 2023} \cdot 2022 \cdot 2023+2023=-1+2023=2022
\end{aligned}
$$

Answer. 2022.