SOLUTION: Hey i would really really really appreciate some help, test tomorrow! (e^t

SOLUTION: Hey i would really really really appreciate some help, test tomorrow! (e^t - e^-t )/ 3 =2

Question 3225: Hey i would really really really appreciate some help, test tomorrow!
(e^t - e^-t )/ 3 =2
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
(e^t - e^-t )/ 3 =2
Let u = e^t, we have e^-t = 1/u,
so (u - 1/u)/3 = 2,
Cancelling the denominator by multiply 3u,
u^2 - 1 = 6u or
u^2 -6u - 1 = 0,
By quadratic formula
u = 3 + sqrt(10) or 3 - sqrt(10)(negative ,invalid)

Since u = e^t = 3 + sqrt(10), so t = ln [3 + sqrt(10)]...Answer
Check, t = ln 3, e^t = 3 + sqrt(10),
e^t = -3 + sqrt(10)
(e^t - e^-t )/ 3 = (3 - (-3))/3 = 2..correct
Kenny
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