SOLUTION: a) solve the equation 7e^x + 3 = 2e^2x b) solve 1/2 |2-2x|<_4 and represent on the number line c) sole the equation x^4-5x^3+5x^2-5x-6=0

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Question 1116196: a) solve the equation 7e^x + 3 = 2e^2x
b) solve 1/2 |2-2x|<_4 and represent on the number line
c) sole the equation x^4-5x^3+5x^2-5x-6=0
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
solve the equation 7e^x + 3 = 2e^2x
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2e^2x - 7e^x - 3 = 0
Sub for e^x
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=73 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3.88600093632938, -0.386000936329383. Here's your graph:

==================
e^x = ~ 3.886
x = ln(3.886) = 1.357
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Ignore the negative value.
===============
sole the equation x^4-5x^3+5x^2-5x-6=0
----
There are no integer zeroes.
Iterative or graphical methods can be used.
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