Question

The sum of a number and its reciprocal is 4.25; the number is ______.

Options

• 2 or `1/2`

• 4 or `1/4`

• `1/5` or 5

• `1/3` or 3

Answer 1

The sum of a number and its reciprocal is 4.25; the number is `underlinebb(4 or 1/4)`.

Explanation:

Let the number be x

Then `x + 1/x = 4.25 = 425/100 = 17/4`

`\implies (x^2 + 1)/x = 17/4`

`\implies` 4(x² + 1) = 17x

`\implies` 4x² + 4 – 17x = 0

`\implies` 4x² – 16x – x + 4 = 0

`\implies` 4x(x – 4) – 1(x – 4) = 0

`\implies` (x – 4)(4x – 1) = 0

Either x – 4 = 0 or 4x – 1 = 0

`\implies x = 4` or `x = 1/4`

`\implies x = 4` or `1/4`