2.9. Solve the equation $\sqrt{2 x-6}+\sqrt{x+4}=5$.

### 2.10. Solve the equation

$$
\sqrt[m]{(1+x)^{2}}-\sqrt[m]{(1-x)^{2}}=\sqrt[m]{1-x^{2}}
$$
2.9. Let $y=\sqrt{x+4}$. Then $x=y^{2}-4$, so $2 x-6=2 y^{2}-$ -14. Therefore, we get the equation $\sqrt{2 y^{2}-14}+y=5$. Move $y$ to the right side and square both sides. As a result, we get the equation $y^{2}+10 y-39=0$. Its roots are 3 and -13. But $y \geqslant 0$, so only the root $y=3$ remains, which corresponds to $x=5$. It is easy to verify that $x=5$ is indeed a root of the given equation.