SOLUTION: I need to solve the following: {{{ e^x }}}-{{{ 1/e^x }}}=2 *I had to write this differently because of the formula plotting system (the second part is really e to the -x inst

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I need to solve the following: {{{ e^x }}}-{{{ 1/e^x }}}=2 *I had to write this differently because of the formula plotting system (the second part is really e to the -x inst      Log On


   

Question 465502: I need to solve the following:
+e%5Ex+-+1%2Fe%5Ex+=2
*I had to write this differently because of the formula plotting system (the second part is really e to the -x instead of 1/e^x).
So I believe from here you subtract 2 from both sides and end up with everything equal to zero, and then you would let u=+e%5Ex+, so that you have u-(1/u)-2=0. Then I get confused as to how to solve this by using the quadratic formula, because I don't know what b=? . That is really all I am confused on, assuming I'm going about this the right way in the first place.
I hope I've explained that well. Thanks!
Jessica
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+e%5Ex+-+1%2Fe%5Ex+=2
Multiply thru by e^x
e%5E%282x%29+-+1+=+2e%5Ex
e%5E%282x%29+-+2e%5Ex+-+1+=+0
Sub u for e^x
u%5E2+-+2u+-+1+=+0
u = 1 +/- sqrt(2)
x = ln(1 +/- sqrt(2))
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PS hyp cos(x) = %28e%5Ex+%2B+e%5E%28-x%29%29%2F2%29
hyp sin(x) = %28e%5Ex+-+e%5E%28-x%29%29%2F2%29