Question

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

Answer 1

Answer:

The positive integers are 8 and 4

Step-by-step explanation:

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

$x = 2y$

The difference of their reciprocals is 1/8.

$\frac{1}{y} - \frac{1}{x} = \frac{1}{8}$

Multiply through the second equation by 8xy

$8x - 8y = xy$

Substitute the first equation into this last equation:

$8(2y) - 8y = 2y \times y$

$16y - 8y = {2y}^{2}$

$8y = 2{y}^{2}$

$4y = {y}^{2}$

${y}^{2} - 4y = 0$

$y(y - 4) = 0$

$y = 0$

or

$y = 4$

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

Therefore y=4 and x=8