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?
+4622 1/x + 1/y = 1/18
\(\frac{x+y}{xy}=\frac{1}{18}\).
\(18x+18y=xy\)
\(xy-18x-18y=0\)
Note that the expression is very close to \((x-18)(y-18)\) is if I add 324 to both sides.
\((x-18)(y-18)=324\).
324=2^2*3^4
12+18=30
27+18=45
30 and 45 give the largest result, thus x+y=30+45=75.
