2. Solve the inequality (9 points):

$$
\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x-1}}}} \geq \sqrt{1+\sqrt{2}}
$$
# Solution:

The left side increases and at $x=1$ it is exactly equal to the right side.

Answer: $x \geq 1$.

| Points | Criteria for evaluating the completion of task № 2 |
| :---: | :--- |
| $\mathbf{9}$ | A correct and justified sequence of all steps of the solution is provided. The correct answer is obtained. |
| $\mathbf{5}$ | The problem is not solved, but its solution is significantly advanced, i.e.:  - a significant part of the solution is performed correctly, possibly inaccurately (for example, the increase of the function on the left side of the inequality is established or the domain of the inequality is found and initial transformations are performed correctly);  - the other part is either not performed or performed incorrectly, possibly even with logical errors (for example, the solution of the inequality is not found or contains logical errors).  The solution may be incomplete. |
| $\mathbf{0}$ | All cases of the solution that do not meet the criteria for scoring 5 and 9 points. |