Answer:
The positive integers are 8 and 4
Step-by-step explanation:
Let the bigger integer be x, and the smaller be y, then
[tex]x = 2y[/tex]
The difference of their reciprocals is 1/8.
[tex] \frac{1}{y} - \frac{1}{x} = \frac{1}{8} [/tex]
Multiply through the second equation by 8xy
[tex]8x - 8y = xy[/tex]
Substitute the first equation into this last equation:
[tex]8(2y) - 8y = 2y \times y[/tex]
[tex]16y - 8y = {2y}^{2} [/tex]
[tex]8y = 2{y}^{2} [/tex]
[tex]4y = {y}^{2} [/tex]
[tex] {y}^{2} - 4y = 0[/tex]
[tex]y(y - 4) = 0[/tex]
[tex]y = 0[/tex]
or
[tex]y = 4[/tex]
But y≠0, since division by zero is not defined.
Therefore y=4 and x=8
