It is a hard problem. There are some hints in the answer key page for this problem.
Let a be the integer part of the number and b be the decimal part. The number can then be written as a + b.
Since the three terms of b, a, and a+b form a geometric sequence, the following equation is true: a^2 = b(b+a).
Dividing both sides of the equation by a^2 you will get another equation.
Following the steps as shown in page 8 of the book, you will get the final result.
Good luck!