SOLUTION: Find two positive real numbers that differ by 2 and have a product of 10

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Question 286544: Find two positive real numbers that differ by 2 and have a product of 10
Found 2 solutions by richwmiller, Fombitz:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
a-b=2
a*b=10
a=2+b
(2+b)*b=10
2b+b^2=10
b^2+2b-10=0
b=2.31662
a=4.31662
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=44 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2.3166247903554, -4.3166247903554. Here's your graph:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!



Use the quadratic formula,





Since only positive numbers are acceptable,

or approximately the two numbers are,
X=2.317
X+2=4.317
X(X+2)=10.002
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