I need help on a question

[wxc0212]

While doing some practice questions my mom printed out for me i ran accross a question that i wasn't able to figure out.
Here's the question:

A positive number has a decimal part and an integer part. The decimal part, the integer part, and the positive number itself form a geometric sequence. Find this positive number.

Could someone please help. Thank you!

[yongcheng3315]

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!