Question

If a number is added to three times its reciprocal, the result is `5 3/5`. Find the number.

Answer 1

Given:

Three times its reciprocal is `3/x`

Let the number be x.

`x + 3/x = 5 3/5`

`5 3/5 = 28/5`

`x + 3/x = 28/5`

Multiply both sides by 5x:

5x² + 15 = 28x

5x² − 28x + 15 = 0

Solve the quadratic equation

(5x − 3) (x − 5) = 0

`x = 3/5 or x = 5`

The required number is:

5 or `3/5`