Given positive integers x and $y$ such that $x\neq y$ and 1/x + 1/y = 1/8, what is the smallest possible value for x + y?
+23252 1/x + 1/y = 1/8 ---> 1/y = 1/8 - 1/x
1/y = (x - 8) / 8x
y = 8x / (x - 8)
x + y = x + 8x / (x - 8) ---> x + y = [ x(x - 8) ] / (x - 8) + 8x / (x - 8)
= (x2 - 8x + 8x) / (x - 8)
= x2 / (x - 8)
For values between 0 and 8, the value of x + y is negative.
For values above 8, the value is positive and increasing.
Thus, the smallest value of x + y occurs at the integer value x = 9.
You can find this value ...
