SOLUTION: For all positive integers x and y such that 1/x + 1/y = 1/12, find the greatest value that y can have. What is the way to do this? Thanks!

Question 1048379: For all positive integers x and y such that 1/x + 1/y = 1/12, find the greatest value that y can have.
What is the way to do this? Thanks!
Found 2 solutions by josgarithmetic, robertb:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Do you need a specific way of dealing with this, or is making a graph acceptable and looking for integer points?

12xy is common denominator.

but does this have a maximum?
, derivative, Quotient Rule.

------THIS IS NEVER 0.
But you are looking for POSITIVE integers.

You could try positive integers x starting with 0, on . Would any acceptable y, integer, also be positive?

NO.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

<===> <===> .
Since x and y are positive integers, x-12 must divide 12.
===> x-12 = 1,2,3,4,6,12
Obviously, the value of x-12 that would maximize y is 1, which would give x = 13. The corresponding value of y would be 156.
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