Question 58
Find all values of $a$, for which the equation
$$
\frac{2 a}{(x+1)^{2}}+\frac{a+1}{x+1}-\frac{2(a+1) x-(a+3)}{2 x^{2}-x-1}=0
$$
has two real roots $x_{1}$ and $x_{2}$ satisfying the relation $x_{2}^{2}-a x_{1}=a^{2}-a-1$.
$$
\frac{2 a}{(x+1)^{2}}+\frac{a+1}{x+1}-\frac{2(a+1) x-(a+3)}{2 x^{2}-x-1}=0
$$
has two real roots $x_{1}$ and $x_{2}$ satisfying the relation $x_{2}^{2}-a x_{1}=a^{2}-a-1$.