3. Solve the equation

$$
\sqrt{\frac{x-3}{11}}+\sqrt{\frac{x-4}{10}}+\sqrt{\frac{x-5}{9}}=\sqrt{\frac{x-11}{3}}+\sqrt{\frac{x-10}{4}}+\sqrt{\frac{x-9}{5}}
$$
Answer: 14.

Solution. If we perform the variable substitution $x=t+14$, 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 side of the equation is greater, and for $-2 \leqslant t<0$ the left side is greater. Therefore, the only solution is $t=0$, which implies $x=14$.

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