SOLUTION: the product of two numbers is 48. One number is 2 less than the other. what are the numbers? a X b = 48 , a = b - 2 , (b - 2) x b = 48

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Question 818671: the product of two numbers is 48. One number is 2 less than the other. what are the numbers? a X b = 48 , a = b - 2 , (b - 2) x b = 48
Answer by jhunjiro(67) About Me  (Show Source):
You can put this solution on YOUR website!
Solution:
(b - 2) x b = 48
b^2 -2b=48
b^2-2b-48=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ab%5E2%2Bbb%2Bc=0 (in our case 1b%5E2%2B-2b%2B-48+=+0) has the following solutons:

b%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-48=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+196+%29%29%2F2%5Ca.

b%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+196+%29%29%2F2%5C1+=+8
b%5B2%5D+=+%28-%28-2%29-sqrt%28+196+%29%29%2F2%5C1+=+-6

Quadratic expression 1b%5E2%2B-2b%2B-48 can be factored:
1b%5E2%2B-2b%2B-48+=+1%28b-8%29%2A%28b--6%29
Again, the answer is: 8, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-48+%29


Final Answer:
b=8
a=6