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.

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