Answer
Please see the work below.
Work Step by Step
(a) We know that
$U=-\int Fdx$
$U=-\int (\frac{A}{x^2})dx$
$U=\frac{A}{x}$
Thus, the potential energy difference is:
$\Delta U=\frac{A}{x_2}-\frac{A}{x_1}$
(b) The potential energy difference is given as
$\Delta U=\frac{A}{\infty}-\frac{A}{x_1}=-\frac{A}{x_1}$
