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Rsok96
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?
It means of all the options, when you multiply them, it gives the lowest result.
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
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.
thank you to everyone who answered they were all helpful