Answer:
-8.5 and 7.5
Explanation:
Let's call the two numbers x and y. We know that their difference is 16, so we can write:
x - y = 16 or x = y + 16
We want to find the values of x and y that minimize the expression:
x + y + xy
Substituting x = y + 16, we get:
(y + 16) + y + (y + 16)y
Simplifying and expanding, we get:
y^2 + 17y + 16
To minimize this expression, we can take its derivative with respect to y and set it equal to 0:
d/dy (y^2 + 17y + 16) = 2y + 17 = 0
Solving for y, we get:
y = -8.5
Substituting y = -8.5 into x = y + 16, we get:
x = 7.5
Therefore, the two numbers with a difference of 16 such that the result of adding their sum and their product is a minimum are -8.5 and 7.5.