2. Solve the equation $\frac{15}{x\left(\sqrt[3]{35-8 x^{3}}\right)}=2 x+\sqrt[3]{35-8 x^{3}}$. Write the sum of all obtained solutions in the answer.

(5 points)

#
# Solution.

$$
u=\sqrt[3]{35-8 x^{3}}, 8 x^{3}=35-u^{3}
$$

$\left\{\begin{array}{c}\frac{15}{x u}=2 x+u, \\ 8 x^{3}+u^{3}=35,\end{array} t=2 x u, v=2 x+u \Rightarrow\left\{\begin{array}{c}\frac{30}{t}=v, \\ v\left(v^{2}-3 t\right)=35,\end{array} \Rightarrow\left\{\begin{array}{l}t=6, \\ v=5,\end{array}\right.\right.\right.$

$$
\left\{\begin{array}{c}
x u=3, \\
2 x+u=5
\end{array} \Rightarrow 2 x^{2}-5 x+3=0 \Rightarrow x_{1}+x_{2}=2.5\right.
$$

## Answer: 2.5