SOLUTION: a student multiplies 3 numbers and the result is 45. one of the number is 4 and the other two numbers one is greater than the other by 6, what are the two numbers?

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Question 989159: a student multiplies 3 numbers and the result is 45. one of the number is 4 and the other two numbers one is greater than the other by 6, what are the two numbers?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
x=smaller number
(4)(x)(x+6)=45
4x^2+24x=45
4x^2+24x-45=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B24x%2B-45+=+0) has the following solutons:

x%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=%2824%29%5E2-4%2A4%2A-45=1296.

Discriminant d=1296 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-24%2B-sqrt%28+1296+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2824%29%2Bsqrt%28+1296+%29%29%2F2%5C4+=+1.5
x%5B2%5D+=+%28-%2824%29-sqrt%28+1296+%29%29%2F2%5C4+=+-7.5

Quadratic expression 4x%5E2%2B24x%2B-45 can be factored:
4x%5E2%2B24x%2B-45+=+4%28x-1.5%29%2A%28x--7.5%29
Again, the answer is: 1.5, -7.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B24%2Ax%2B-45+%29

x=1.5 or -7.5
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For x=1.5, x+6=7.5 : For x=-7.5, x+6=-1.5
ANSWER: The other two numbers are 1.5 and 7.5 or -1.5 and -7.5.