SOLUTION: The difference between two positive integers is 5 and the difference between their reciprocals is 5/24. Find the integers.

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Question 1151014: The difference between two positive integers is 5 and the difference between their reciprocals is 5/24. Find the integers.
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.

x - y = 5            (1)

1%2Fy - 1%2Fx = 5%2F24         (2)


From equation (2),

%28x+-+y%29%2F%28xy%29 = 5%2F24.


Replace here x-y in the numerator by 5, based on (1).  You will get

    5%2Fxy = 5%2F24,


which implies

    xy = 24.    (3).



Now the problem is to find two positive integers with the difference 5 and the product 24.


It requires 5 seconds to guess the ANSWER mentally :  the numbers are  3 and 8.



Or, if you want to solve it algebraically, write this quadratic equation

    x*(x-5) = 24


and complete the solution by a standard way.