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Leokris [45]
3 years ago
6

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

Mathematics
1 answer:
Temka [501]3 years ago
7 0

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

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