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

Question 260165: find 2 numbers whose sum is 18 and product is 20.
Found 2 solutions by Alan3354, unlockmath:
Answer by Alan3354(69443) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=244 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 16.8102496759067, 1.18975032409335. Here's your graph:

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and

Answer by unlockmath(1688) (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
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