Find two positive numbers whose product is 81 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.)

Answer 1

9,9

a square has minimum perimeter for a given area

Answer 2

let one number be x, then the other is 81/x

sum = x + 81/x
d(sum)/dx = 1 - 81/x^2
= 0 for a min
1 = 81/x^2
x^2 = 81
x = 9 , since x must be positive

so if one is 9, the other is 81/9 which is also 9