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find two numbers whose sum is 55 and whose product is 684
Call the numbers x and y.
x+y = 55
xy = 684
From the 1st eqn, y = 55-x
Sub that into the 2nd eqn
x*(55-x) = 684
55x - x^2 = 684
x^2 - 55x + 684 = 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=289 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 36, 19.
Here's your graph:
The graph isn't much help, but the numbers are given:
19 and 36