Question

Find two positive numbers whose product is 225 and whose sum is a minimum

Answer 1

Let S = x + y.
 
Since xy = 225, y = 225/x.
Substitute into the sum to get S = x + 225/x.
Then S' = 1 - 225/x^2, implying that 15/x = 1.
Then x = 15.
 The other number is also 15.