Of all the numbers whose difference is 36 , find the two that have the minimum product

54,18

Step-by-step explanation:

Let one of the numbers be x. The other number be represented as 36-x

(x - (36-x) = 36

open brackets

x - 36 + x = 36

x + x = 36 + 36 = 72

2x = 72

x = 72/2 = 36

x = 36

The product can then be represented as y = x (36-x) or y=36x-x²

The maximum or minimum is always on the axis of symmetry which has the formula x=-b/2a.

In our case, the axis of symmetry is - 36/-2, so x=18.

If one number is 18 and the 2 numbers differentiate by 36, the other number is 18 + 36 = 54

So the 2 numbers are 18 and 54 and the minimum product is 972