# SOLUTION: Find two real numbers that have a sum of 6 and a product of 4.

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Question 212506: Find two real numbers that have a sum of 6 and a product of 4.
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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

Substitute

Step 5. Now use above equation to obtain a quadratic one.

Add 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!

Respectfully,
Dr J