SOLUTION: find 2 numbers whose sum is 18 and product is 20.

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Question 260165: find 2 numbers whose sum is 18 and product is 20.
Found 2 solutions by Alan3354, unlockmath:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find 2 numbers whose sum is 18 and product is 20.
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x(18-x) = 20
x^2 - 18x + 20 = 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-18x%2B20+=+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=%28-18%29%5E2-4%2A1%2A20=244.

Discriminant d=244 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--18%2B-sqrt%28+244+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+244+%29%29%2F2%5C1+=+16.8102496759067
x%5B2%5D+=+%28-%28-18%29-sqrt%28+244+%29%29%2F2%5C1+=+1.18975032409335

Quadratic expression 1x%5E2%2B-18x%2B20 can be factored:
1x%5E2%2B-18x%2B20+=+%28x-16.8102496759067%29%2A%28x-1.18975032409335%29
Again, the answer is: 16.8102496759067, 1.18975032409335. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-18%2Ax%2B20+%29

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9+%2B+sqrt%2861%29 and
9+-+sqrt%2861%29



Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
Let's set up two equations and solve it from there.
x+y=18
xy=20
There are a couple ways to solve this. Let's set the first one like this:
x+y=18 Subtract y from both sides to give:
x=18-y Replace this into the second equation as:
(18-y)y=20 rewritten as
18y-y^2=20 Move these so they equal zero.
0=y^2-18y+20 Now we use the quadratic equation to solve:
y = (-b +- sqrt( b^2-4*a*c ))/(2*a) }
y = (18 +- sqrt( 324-80)/(2) Rewritten as:
y = (18 +- sqrt 244)/2 (Sqrt of 244 is approx 15.65)
y = 1.18975 (Approx)
Now solve for x
I'm doing basically the same as I solved for y but won't show all the steps here.
x= 16.81024 (approx)
Now we can add these and multiply these answers and it will work out.
Very good Problem.
RJ
Check out a new book I wrote at:
www.math-unlock.com