Question

find two numbers whose product is N^2 and whose sum is a minimum

Answer 1

let one number be x, then the other is n^2/x
sum = x + n^2/x
d(sum)/dx = 1 - n^2/x^2 = 0 for a minimum
n^2/x^2 = 1
n/x = ± 1

x = N or x = -N

e.g. If N^2 = 144
then both numbers would be 12 (or
both numbers would be -12)

factors of 144
= 12x12 ---- sum = 24
= 4x36 ---- sum = 40
= 8x18 --- sum = 26
etc.