3. Solve the equation:

$$
\frac{1}{\sqrt{5^{x}+12^{x}}}+\sqrt{x+7}=\frac{14}{13}+\sqrt{x+2}
$$
3. $\frac{1}{\sqrt{5^{x}+12^{x}}}+\sqrt{x+7}-\sqrt{x+2}=\frac{14}{13}$ or $\frac{1}{\sqrt{5^{x}+12^{x}}}+\frac{5}{\sqrt{x+7}+\sqrt{x+2}}=\frac{14}{13}$ $.2 p$

$x=2$ verifies the equation, and the function on the left side is strictly decreasing, so $x=2$ is the only solution

$5 p$