Question

The difference between two positive integers is 4 and the difference between their reciprocal is 1/24 , find the 2 integers .

Answer 1

x - y = 4
1/y - 1/x = 1/24
x = y + 4
1/y - 1/(y + 4) = 1/24
(y + 4)/y - 1 = (y + 4)/24
y/y + 4/y - 1 = y/24 + 1/6
4/y = y/24 + 1/6
4 = y^2/24 + y/6
96 = y^2 + 4y
y^2 + 4y -96 = 0
(y + 12)(y - 8) = 0

The numbers are 8 and 12

Answer 2

heres the answer
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