Given positive integers x and y such that x is not equal to y and 1/x + 1/y = 1/20, what is the smallest possible value for x + y ?
+130071 Let 20 = z
Let x = a + z
Let y = b + z
So we have
1/ ( a + z) + 1/ (b + z) = 1 / z simplifying we have
[a + b + 2z ] z = (a + z) ( b + z)
az + bz + 2z^2 = ab + az + bz + z^2
z^2 = ab
400 = ab
20 * 20 = ab (but a, b are different)
Next closest factors of 400 are 25 and 16
a b a + z = x b + z = y
25 16 45 = x 36 = y
x + y = 81 = smallest possible value
