Question

a positive integer is twice another. the sum of the reciprocals of the two positive integers is 1/8. find the two integers

Answer 1

Let the integer is x
So, its twice is 2x
So, the reciprocals of the two integers =
`(1)/(x) \ and \ (1)/(2x)`
The sum of the reciprocals of the two positive integers = 1/8


∴
`(1)/(x) + (1)/(2x) = (1)/(8)`
∴
`(2+1)/(2x) = (1)/(8)`
∴
`(3)/(2x) = (1)/(8)`
∴ 2x = 24
∴ x = 12

So, the two integers are 12 and 24