SOLUTION: 2e^x-2e^-x=5 2e^x-2/e^x=5 let e^x=y. 2y-2/y=5 2y^2-2=5y 2y^2-5y-2=0

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Question 526583: 2e^x-2e^-x=5
2e^x-2/e^x=5
let e^x=y.
2y-2/y=5
2y^2-2=5y
2y^2-5y-2=0
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
2e^x-2e^-x=5
2e^x-2/e^x=5
let e^x=y.
2y-2/y=5
2y^2-2=5y
2y^2-5y-2=0
Good so far.
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=41 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2.85078105935821, -0.350781059358212. Here's your graph:

---------------
e^x = the solutions
x = ln of the positive solution
x =~ ln(2.85)
x =~ 1.04732
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