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!