SOLUTION: Find two real numbers that have a sum of 8 and a product of 2.

Question 153155: Find two real numbers that have a sum of 8 and a product of 2.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Find two real numbers that have a sum of 8 and a product of 2.
.
Let x = one of two real numbers
and y - second of two real numbers
.
Since we have two unknowns, we'll need two equations.
.
From:"that have a sum of 8" we get equation 1:
x + y = 8
.
From:"product of 2" we get equation 2:
xy = 2
.
Solving equation 1 for y:
x + y = 8
y = 8-x
.
Plug the above into equation 2 and solve for x:
xy = 2
x(8-x) = 2
8x-x^2 = 2
0 = x^2 - 8x + 2
Since, we can't factor, we must use the quadratic equation.
x = {7.742, 0.258}
y = (0.258, 7.742)
.
Answer: the two numbers are 7.742 and 0.258
.
Details of quadratic solution follows:

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=56 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7.74165738677394, 0.258342613226059. Here's your graph:

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