Question

The sum of a number and its reciprocal is `13/6`. Find the number.

Answer 1

Let a number be x.

According to the question,

`x/1 + 1/x = 13/6`

`(x^2 + 1)/x = 13/6`

6(x² + 1) = 13x

6x² + 6 = 13x

6x² – 13x + 6 = 0

6x² – 9x – 24x + 6 = 0

3x(2x – 3) – 2(2x – 3) = 0

(2x – 3)(3x – 2) = 0

2x – 3 = 0 or 3x – 2 = 0

⇒ 2x = 3

x = `3/2`

⇒ 3x = 2

x = `2/3`

Number is `3/2` or `2/3`.