Given positive integers x and y such that x not equal to y and 1/x + 1/y = 1/20, what is the smallest possible value for x + y?
Given positive integers x and y such that x not equal to y and 1/x + 1/y = 1/20, what is the smallest possible value for x + y?
We need to have a total that will reduce to 1/20. 2/40 won't work because that requires x and y to be the same.
How about 60. 3/60 will break up into 2/60 + 1/60 which adds to 3/60 but that has both x and y being 60.
So reduce 2/60 to 1/30. Now x and y are different.
1 1 3 1
So ––– + ––– = ––– = –––
30 60 60 20 This arrangement makes x + y = 90
.
