SOLUTION: Find the two numbers whose product is 3 and the larger number is 10 more than the smaller number.

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Question 587957: Find the two numbers whose product is 3 and the larger number is 10 more than the smaller number.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the two numbers whose product is 3 and the larger number is 10 more than the smaller number.
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x*(x+10) = 3
x%5E2+%2B+10x+-+3+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B10x%2B-3+=+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=%2810%29%5E2-4%2A1%2A-3=112.

Discriminant d=112 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+112+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+112+%29%29%2F2%5C1+=+0.291502622129181
x%5B2%5D+=+%28-%2810%29-sqrt%28+112+%29%29%2F2%5C1+=+-10.2915026221292

Quadratic expression 1x%5E2%2B10x%2B-3 can be factored:
1x%5E2%2B10x%2B-3+=+%28x-0.291502622129181%29%2A%28x--10.2915026221292%29
Again, the answer is: 0.291502622129181, -10.2915026221292. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B-3+%29

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