Question

If the difference between a number and its reciprocal is `24/5`, find the number

Answer 1

Let the number be “x” and its reciprocal is `1/x`

By the given condition

`x - 1/x = 24/5`

`(x^2 - 1)/x = 24/5`

5x² – 5 = 24x

5x² – 24x – 5 = 0

5x² – 25x + x – 5 = 0

⇒ 5x(x – 5) + 1(x – 5) = 0

(x – 5) (5x – 1) = 0

⇒ x – 5 = 0 or 5x + 1 = 0

x = 5 or 5x = – 1

⇒ x = `(-1)/5`

The number is 5 or `(-1)/5`