SOLUTION: two numbers their sum is 43 and their product is 405 . what are the difference of this two numbers ?

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Question 435201: two numbers their sum is 43 and their product is 405 . what are the difference of this two numbers ?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x(43-x) = 405
x%5E2+-+43x+%2B+405+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-43x%2B405+=+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=%28-43%29%5E2-4%2A1%2A405=229.

Discriminant d=229 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--43%2B-sqrt%28+229+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-43%29%2Bsqrt%28+229+%29%29%2F2%5C1+=+29.0663729752108
x%5B2%5D+=+%28-%28-43%29-sqrt%28+229+%29%29%2F2%5C1+=+13.9336270247892

Quadratic expression 1x%5E2%2B-43x%2B405 can be factored:
1x%5E2%2B-43x%2B405+=+%28x-29.0663729752108%29%2A%28x-13.9336270247892%29
Again, the answer is: 29.0663729752108, 13.9336270247892. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-43%2Ax%2B405+%29