2. Solve the equation

$$
\sqrt{\frac{x-2}{11}}+\sqrt{\frac{x-3}{10}}=\sqrt{\frac{x-11}{2}}+\sqrt{\frac{x-10}{3}}
$$
Answer: 13.

Solution. If we perform the variable substitution $x=t+13$, then in all the expressions under the square roots, 1 will be factored out:

$$
\sqrt{\frac{t}{11}+1}+\sqrt{\frac{t}{10}+1}=\sqrt{\frac{t}{2}+1}+\sqrt{\frac{t}{3}+1}
$$

Now it is clear that for $t>0$ the right side of the equation is greater, and for $-2 \leqslant t \leqslant 0$ the left side is greater. Therefore, the only solution is $t=0$, which implies $x=13$.

Estimation. 12 points for a correct solution. If the answer is guessed but the uniqueness of the solution is not proven, 3 points.

$$
\left(\frac{x-k}{m}>\frac{x-m}{k} \Longleftrightarrow x>k+m\right) \text{ for } (m>0) \Rightarrow\left(\frac{x-k}{m}>\frac{x-m}{k} \Longleftrightarrow x>k+m\right)
$$