SOLUTION: What multiplys to give you -132 but adds to give you 1

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Question 1052999: What multiplys to give you -132 but adds to give you 1
Found 3 solutions by Alan3354, advanced_Learner, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
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Find a pair of factors of 132 that differ by 1.
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The larger factor is negative.

Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
xy=-132
x%2By=1 gives y=1-x
x%281-x%29=-132
%28x-x%5E2%29=-132
%28x%5E2-x-132%29=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-132+=+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=%28-1%29%5E2-4%2A1%2A-132=529.

Discriminant d=529 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+529+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+529+%29%29%2F2%5C1+=+12
x%5B2%5D+=+%28-%28-1%29-sqrt%28+529+%29%29%2F2%5C1+=+-11

Quadratic expression 1x%5E2%2B-1x%2B-132 can be factored:
1x%5E2%2B-1x%2B-132+=+1%28x-12%29%2A%28x--11%29
Again, the answer is: 12, -11. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-132+%29

Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.
12 and -11.