Question

Two numbers have a difference of 8. Find the numbers if their product is a minimum.?

What does the part where it says the product is a minimum mean?
How does that part relate to your answer?

Answer 1

4 and -4?

Answer 2

It means of all the options, when you multiply them, it gives the lowest result.

Answer 3

let the numbers be x and y
x-y=8
so y=x-8

xy=minimum
substitute (x-8) in y
and substitute y for min
x(x-8)=y
y=x^2-8x
now complete the square
y=(x-4)^2-16
x=4
substitute in first equation
4-y=8
y=-4
so the numbers are 4,-4

Answer 4

logically, the largest product is a square. Since you want the lowest, there is a change with one of the numbers being negative (plus/minus version of same number), giving you the largest negative number. So we use our difference to tell us how far in each direction we travel from zero.

Answer 5

thank you to everyone who answered they were all helpful