SOLUTION: diff of two no. is 7. their product is 14. sum of their squares is 77. find two no.s?

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Question 332491: diff of two no. is 7. their product is 14. sum of their squares is 77. find two no.s?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
diff of two no. is 7. their product is 14. sum of their squares is 77.
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y-x = 7 --> y=x+7
x*y = 14
Sub for y
x*(x+7) = 14
x^2 + 7x = 14
x^2 + 7x - 14 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B7x%2B-14+=+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=%287%29%5E2-4%2A1%2A-14=105.

Discriminant d=105 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+105+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+105+%29%29%2F2%5C1+=+1.6234753829798
x%5B2%5D+=+%28-%287%29-sqrt%28+105+%29%29%2F2%5C1+=+-8.6234753829798

Quadratic expression 1x%5E2%2B7x%2B-14 can be factored:
1x%5E2%2B7x%2B-14+=+%28x-1.6234753829798%29%2A%28x--8.6234753829798%29
Again, the answer is: 1.6234753829798, -8.6234753829798. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B-14+%29

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x = 1.623475
y = 8.623475
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x = -1.623475
y = -8.623475