2. Solve the equation $\frac{x}{3}+\frac{x}{\sqrt{x^{2}-9}}=\frac{35}{12}$. Write the sum of all obtained solutions in the answer.

(5 points)
Solution. $\quad x=\frac{3}{\sin t}, t \in\left(0 ; \frac{\pi}{2}\right)$

$$
\begin{gathered}
\frac{1}{\sin t}+\frac{1}{\cos t}=\frac{35}{12}, \quad 24(\sin t+\cos t)=35\left((\sin t+\cos t)^{2}-1\right) \\
z=\sin t+\cos t, 35 z^{2}-24 z-35=0 \\
z_{1}=-\frac{5}{7}, z_{2}=\frac{7}{5}, \sin t+\cos t=\frac{7}{5}
\end{gathered}
$$

$y=\sin t, \quad y+\sqrt{1-y^{2}}=\frac{7}{5}$,

$$
\sin t_{1}=\frac{3}{5}, \sin t_{2}=\frac{4}{5}, \quad x_{1}=5, \quad x_{2}=\frac{15}{4}, x_{1}+x_{2}=5+\frac{15}{4}
$$

## Answer: $\mathbf{8.75}$