Question

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

Answer 1

Answer:

24

Step-by-step explanation:

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.

Answer 2

Step-by-step explanation:

x-y=5

1/x-1/y=5/24

y-x/xy=5/24

24y-24x=5xy

-24x+24y=5xy

-24(x-y) =5xy

xy= -24

so, x=8,y=3

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