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Find two real numbers that have a sum of 6 and a product of 4.
Step 1. Let x be one number
Step 2. Let y be the other number
Step 3. The problem statement gives us that x+y=6 or y=6-x
Step 4. We're also give that
Step 5. Now use above equation to obtain a quadratic one.
to both sides of the equation so left side will = 0
Step 6. So now we have a quadratic equation, so we can use the quadratic formula given as
where a=1, b=-6 and c=4 for our example. Follow steps below:
|Solved by pluggable solver: SOLVE quadratic equation with variable|
|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=20 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 5.23606797749979, 0.76393202250021.
Here's your graph:
Step 7. ANSWER: The above steps give us two numbers : 5.2361 and 0.7639.
You can check to see if these numbers add up to 6 and their products equal 4 as given by the problem.
I hope the above steps were helpful. Good luck in your studies!
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