SOLUTION: The difference of two numbers is -8 and the product is 20. The smallest number is?

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Question 202878: The difference of two numbers is -8 and the product is 20. The smallest number is?
Found 2 solutions by dyakobovitch, MathTherapy:
Answer by dyakobovitch(40)   (Show Source): You can put this solution on YOUR website!
The difference of two numbers is -8 and the product is 20. The smallest number is?

x-y=-8 ; xy=20.

So, x=y - 8. Using substitution, we have:
(y-8)y=20
y^2-8y-20=0
(y-10)(y+2)=0.

Your two numbers are -2 and 10. (Note: It doesn't matter whether x or y is -2 or 10, since you are only looking for the smallest number).

Therefore, your answer is -2.

--
David
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
Since the difference between the 2 numbers is – 8, it means that the larger number is subtracted from the smaller number to get – 8. By letting the smaller number be s, and the larger number l, we have the following equations:

s – l = - 8
sl = 20

Using the 1st equation to solve for l, we get:
- l = - 8 – s
l = 8 + s

Substituting this value, 8 + s for l in equation 2, we get:
s(8 + s) = 20

(s + 10)(s – 2) = 0

s = , or

Therefore, s, or the smaller number can either be – 10, or 2

If the small number is – 10, then the larger number is - 2

Check
s – l = - 8
- 10 - - 2 = - 8
- 10 + 2 = - 8 (TRUE)

sl = 20
- 10 * - 2 = 20 (TRUE)

If the small number is 2, then the larger number is 10

Check
s - l = - 8
2 – 10 = - 8 (TRUE)

sl = 20
2 * 10 = 20 TRUE)
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