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
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