11.2. Solve the equation $(\sqrt{2023}+\sqrt{2022})^{x}-(\sqrt{2023}-\sqrt{2022})^{x}=\sqrt{8088}$.
Answer: $x=1$.

Solution. Notice that $\sqrt{8088}=2 \sqrt{2022}$. This observation suggests that $x=1$ is a root of the equation. We will show that there are no other roots. Indeed, the left side represents the difference of two exponential functions: the base of the first is greater than one, and the base of the second is less than one (it can be noted that the product of these bases equals one). Therefore, the left side is the difference of an increasing and a decreasing function over the entire real line, i.e., it is a strictly increasing function, and thus it takes the value equal to the number on the right side at the unique point $x=1$.