Determine two positive numbers whose product is 100 and whose sum is a minimum.?

Answer 1

let one number be x then 2nd number = 100/x

we need to minimize (x+100/x)
= (x^2+100)/x = (x-10)^2/x + 20 as x^2+100 = (x-10)^2 + 20 x

clearly it is minumum when (x-10) = 0 or x = 10

so 2 numbers are 10 and 10

Answer 2

This is a nice problem in elementary calculus.
We want to minimise x+y subject to xy = 100.
Thus y = 100/x
and we have to minimise
f(x) = x + 100/x on [0,100].
Since x must be positive, neither of the endpoints
works, so we take the derivative:
f'(x) = 1 -100/x² = 0.
Solving,
x² = 100
So x = 10 and y = 10.
The minimal sum is 20.

Answer 3

It seems likely that you are supposed to solve using calculus rather than listing possible solutions. If one number is x, then the other is 100/x, and the sum is x + 100/x. You would like to minimize this function.

Answer 4

minimum of ? i assume you mean whole numbers
lets see 1, 100 sum = 101
2x 50 sum = 52
4 x25 sum = 29
5 x20 sum = 25
10x 10 sum = 20
...id go with two tens...

Answer 5

10 and 10.