3. Solve the equation

$$
\sqrt{\frac{x-2}{11}}+\sqrt{\frac{x-3}{10}}+\sqrt{\frac{x-4}{9}}=\sqrt{\frac{x-11}{2}}+\sqrt{\frac{x-10}{3}}+\sqrt{\frac{x-9}{4}}
$$
Solution. If we perform the variable substitution $x=t+13$, then in all the expressions under the square roots, 1 will be factored out:

$$
\sqrt{\frac{t}{11}+1}+\sqrt{\frac{t}{10}+1}+\sqrt{\frac{t}{9}+1}=\sqrt{\frac{t}{2}+1}+\sqrt{\frac{t}{3}+1}+\sqrt{\frac{t}{4}+1}
$$

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

Estimation. For a correct solution, 13 points. If the answer is guessed but the uniqueness of the solution is not proven, 3 points.