Question 96
Find all values of the real parameter $p$ such that the equation $x^2 + (p^2 + 1)x + p = 2$ has two real distinct roots $x_1$ and $x_2$ such that
$$
\frac{2x_1 - 1}{x_2} + \frac{2x_2 - 1}{x_1} = x_1x_2 + \frac{55}{x_1x_2}.
$$
$$
\frac{2x_1 - 1}{x_2} + \frac{2x_2 - 1}{x_1} = x_1x_2 + \frac{55}{x_1x_2}.
$$