Posted by **cheryl** on Monday, February 14, 2011 at 12:42am.

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

- math -
**Reiny**, Monday, February 14, 2011 at 8:46am
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.

## Answer this Question

## Related Questions

calculus - Find two positive numbers whose product is 100 and whose sum is a ...

Math - Minimizing Sum: Find two positive numbers whose sum is 100 and the sum of...

Math - Find two numbers whose difference is 16, and the sum of whose squares a ...

math - Find two numbers (exactly) whose product is 10 and whose sum is 18.

Calculus - Find two numbers whose difference is 132 and whose product is a ...

math - what are two whole numbers whose product is 1224 and whose sum is 70

math - Leah is throwing discs onto a board numbered 1 to 20. To win a prize she ...

grade 10 math - im stuck in this question,i tried everything but i failed... can...

math - Find three positive real numbers whose sum is 52 and whose product is a ...

math - Find two positive numbers whose sum is 50 such that the sum of their ...