Question
find the real solutions of e^3x-2e^x-3e^-x
Answers
Reiny
I assume you are solving
e^3x-2e^x-3e^-x = 0
multiply each term by e^x
e^(4x) - 2 e^(2x) - 3 = 0
let y = e^(2x) , then we have
y^2 - 2y - 3 = 0
(y - 3)(y + 1) = 0
y = 3 or y = -1
if y = 3
e^(2x) = 3
2x lne = ln3
2x = ln3
<b>x = ln3/2 or appr .5493</b>
or
e^(2x) = -1 <----- no solution
e^3x-2e^x-3e^-x = 0
multiply each term by e^x
e^(4x) - 2 e^(2x) - 3 = 0
let y = e^(2x) , then we have
y^2 - 2y - 3 = 0
(y - 3)(y + 1) = 0
y = 3 or y = -1
if y = 3
e^(2x) = 3
2x lne = ln3
2x = ln3
<b>x = ln3/2 or appr .5493</b>
or
e^(2x) = -1 <----- no solution