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Given positive integers x and y such that x is not equal to y and 1/x + 1/y = 1/12, what is the smallest possible positive value for x + y?

 Oct 2, 2020
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Multiply by 12xy to remove all denominators

12y+12x=xy

So we have xy-12x-12y=0

Add 144

xy-12x-12y+36 = (x-12)(y-12)=144

Note that we can't have 12*12 but we can have 16*9

So x-12 = 16 and y-12 = 9 and x=28, y = 21.

x+y=49

 

You are very welcome!

:P

 Oct 2, 2020
edited by CoolStuffYT  Oct 2, 2020

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