Question

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

Answer 1

Let the numbers be x and `1/x`

Form the given information,

`x + 1/x = 4.25`

`(x^2 + 1)/x = 425/100 = 17/4`

4x² – 17x + 4 = 0

4x² – 16x – x + 4 = 0

4x(x – 4) – 1(x – 4) = 0

(x – 4)(4x – 1) = 0

`x = 4,1/4`

`x = 4 => 1/x = 1/4`

`x = 1/4 => x = 4`

Thus, the number are 4 and `1/4`