Ron G. answered • 04/24/16

Tutor

4.4
(26)
Multiple levels Math, Science, Writing

OK. We start with e

^{x}+e^{-x}=6.I multiplied through by e

^{x}. This led toe

^{2x}- 6e^{x}+ 1 = 0Then I decided to set y = e

^{x}. So now it'sy

^{2}- 6y + 1 = 0This you solve with the Quadratic Formula and get

y = (6 ± √(36 - 4))/2 or y = 5.8 or 0.2 approx.

So e

^{x}= 5.8 or 0.2. This means x = 1.76 or -1.61.Sanity check: I ran this problem through Wolfram Alpha and got ±1.76. This is why you run sanity checks. No doubt I made a rounding error on the negative value. I apologize for that.

Cheers!