Given positive integers x and y such that x not equal to y and 1/x + 1/y = 1/18, what is the smallest possible value for x + y?
1/x + 1/y = 1/18
Note that the expression is very close to \((x-18)(y-18)\) is if I add 324 to both sides.
30 and 45 give the largest result, thus x+y=30+45=75.
Since this is a symmetric equation (you can interchange x and y without changing the equation),
the minimum value will occur when x = y.
Solving 1/x + 1/y = 1/18 ---> 1/x + 1/x = 1/18 ---> 2/x = 1/18 ---> x = 36 ---> x + y = 72.