3. Given $\triangle A B C$ satisfies: $\tan A, \tan B$ are the two roots of the equation $x^{2}-10 x+6=0$, then the value of $\cos C$ is $\qquad$ .
According to the problem, $\left\{\begin{array}{l}\tan A+\tan B=10, \\ \tan A \tan B=6\end{array} \Rightarrow \tan (A+B)=\frac{10}{1-6}=-2 \Rightarrow \tan C=2\right.$ $\Rightarrow \sin C=\frac{2 \sqrt{5}}{5}, \cos C=\frac{\sqrt{5}}{5}$.