math
posted by cheryl on .
find two numbers whose product is N^2 and whose sum is a minimum

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.