3A. Find the relationship between the roots of the quadratic equation

$$
\left(x^{2}-6 m+5\right)+m\left(x^{2}-5 x+6\right)=0
$$

that does not depend on $m$?
Solution. If $m \neq-1$, then the equation is equivalent to the equation

$$
x^{2}-\frac{5 m+6}{m+1} x+\frac{6 m+1}{m+1}=0
$$

and has roots $x_{1}$ and $x_{2}$ for which the equalities hold

$$
x_{1}+x_{2}=\frac{5 m+6}{m+1}=5+\frac{1}{m+1}, \quad x_{1} x_{2}=\frac{6 m+5}{m+1}=6-\frac{1}{m+1}
$$

If we add these two equalities, we get $x_{1}+x_{2}+x_{1} x_{2}=11$.