Let the number we have to find be N.

The sum of the number and its reciprocal is 13/6

=> N + 1/N = 13/6

=> N^2 + 1 = (13/6)N

=> 6N^2 + 6 = 13N

=> 6N^2 - 13N + 6 = 0

=> 6N^2 - 9N - 4N + 6 = 0

=> 3N(2N - 3) - 2(2N - 3) = 0

=> (3N - 2)(2N - 3) = 0

=> N = 2/3 and 3/2

**The required number is 2/3 or 3/2**

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now