Posted by **Sean** on Thursday, June 16, 2011 at 2:50pm.

Find the solution where x and y are integers to:

1/x + 1/y = 1/14

I can use a computer to get a list of solutions:

7, -14

10, -35

12, -84

13, -182

15, -210

16, 112

18, 63

21, 42

28, 28

but I'm having trouble solving this analytically and coming to a general formula.

- math -
**Anonymous**, Thursday, June 16, 2011 at 3:18pm
1/x + 1/y = 1/14

(x+y)/xy=1/14 Inverse

xy/(x+y)=14

xy=14x+14y

xy-14x=14y

x(y-14)=14y

xy=14x+14y

xy-14y=14x

y(x-14)=14x Divide with (x-14)

y=14x/(x-14)

Solutions:

x-14#0

and

y=14x/(x-14) x#0

- math -
**MathMate**, Thursday, June 16, 2011 at 3:30pm
Do not forget that, since x and y are symmetric, they are interchangeable on your list.

Example: if (13, -182) works, then (-182, 13) works as well.

- math -
**Bosnian**, Thursday, June 16, 2011 at 3:36pm
Go to:

wolframalpha com

When page be open in rectangle type:

1/x + 1/y = 1/14

and click option =

When you see results couple times click option: More Solutions

- math -
**Sean**, Thursday, June 16, 2011 at 3:47pm
bosnian, i already used wolfram alpha to get the solutions I listed. I want to derive the solution analytically.

anon, I believe you just did algebraic rearrangement.

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