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
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.
4 answers
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.
Example: if (13, -182) works, then (-182, 13) works as well.
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
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
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.
anon, I believe you just did algebraic rearrangement.