SOLUTION: Find 2 numbers whose difference is 8 and whose product is a minimum. (Hint: Let x be the first number and x+8 be the second number) The answer is 4 and -4, please tell me ho

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Question 1120707: Find 2 numbers whose difference is 8 and whose product is a minimum.
(Hint: Let x be the first number and x+8 be the second number)
The answer is 4 and -4, please tell me how to solve it.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Numbers, x and x+8
Product, x(x+8)

Product is a parabola function with zeros at 0 and -8, for x.
MINIMUM occurs in the exact middle of these two zeros, which will be AT .

4 is not an answer for the minimum.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Find 2 numbers whose difference is 8 and whose product is a minimum.
(Hint: Let x be the first number and x+8 be the second number)
The answer is 4 and -4, please tell me how to solve it.
As instructed, x is the smaller number, and x + 8 is the larger number 

We then get: y = x(x + 8)



We use the formula for the x-coordinate of the vertex of a parabola/axis of symmetry, or  to get x, or the SMALLER number.

So, we get: x, or smaller number = 

LARGER number: 



Regardless of what the expressions are, x being the SMALLER number, and x + 8, the LARGER number, 

or x being the LARGER number, and x - 8, the smaller number, the 2 numbers will be - 4 and 4 

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