Suppose that a is a positive integer and that x and y are positive real numbers such that x*y = a. Then what is the minimum value of (x+y)?
Intuitively, it seems obvious that the minimum positive value of x + y would exist when both x and y are equal to the positive square root of a. But if this is true how would you prove it? And, if not how can the minimum value of x + y be found?