Find two numbers A and B (with A≤B) whose difference is 38 and whose product is minimized

Question

Find two numbers  and  (with ) whose difference is 38 and whose product is minimized

Answer 1

A<B

B-A = 38

B + 38 + A

AB= 38A + A²

The minimum will occurs when the derivative is 0, i.e. 38 + 2A = 0