anonymous
  • anonymous
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?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
4 and -4?
anonymous
  • anonymous
It means of all the options, when you multiply them, it gives the lowest result.
lalaly
  • lalaly
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

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anonymous
  • anonymous
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.
anonymous
  • anonymous
thank you to everyone who answered they were all helpful

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