Question

A positive integer is twice another the difference of the reciprocal of the to positive integer is 1/8

Answer 1

The positive integers are 8 and 4

Explanation:

Let the bigger integer be x, and the smaller be y, then

`x = 2y`

The difference of their reciprocals is 1/8.

`(1)/(y) - (1)/(x) = (1)/(8)`

Multiply through the second equation by 8xy

`8x - 8y = xy`

Substitute the first equation into this last equation:

`8(2y) - 8y = 2y * y`

`16y - 8y = {2y}^(2)`

`8y = 2{y}^(2)`

`4y = {y}^(2)`

`{y}^(2) - 4y = 0`

`y(y - 4) = 0`

`y = 0`

or

`y = 4`

But y≠0, since division by zero is not defined.

Therefore y=4 and x=8