Question

The sum of a number and its reciprocal is 5.2. The number is ______.

Options

• `5 or 1/5`

• `2 or 1/2`

• `4 or 1/4`

• `-2 or -1/2`

Answer 1

The sum of a number and its reciprocal is 5.2. The number is `underlinebb(5 or 1/5)`.

Explanation:

Let the required number be x

Then, according to given condition, we have

`x + 1/x = 5.2 = 52/10 = 26/5`

`\implies (x^2 + 1)/x = 26/5`

`\implies` 5(x² + 1) = 26x

`\implies` 5x² + 5 – 26x = 0

`\implies` 5x² – 26x + 5 = 0

`\implies` 5x² – 25x – x + 5 = 0

`\implies` 5x(x – 5) – 1(x – 5) = 0

`\implies` (x – 5)(5x – 1) = 0

Either x – 5 = 0 or 5x – 1 = 0

`\implies` x = 5 or x = `1/5`

`\implies` x = 5 or `1/5`