Question 168634
e^x + e^(-x) = 5

e^x + 1/e^x = 5
Multiply thru by e^x to get:

e^2x + 1 = 5 e^x
Rearrange to form a quadratic equation:

(e^x)2 - 5e^x + 1 = 0
---------------------------
Change the variable: Let w = e^x
Rewrite:
w^2 - 5w + 1 = 0
Use the quadratic formula:
w = [5 +- sqrt(25-4*1)]/2
w = [5 +- sqrt(21)]/2
--------------------------
Change back to e^x
e^x = [5 + sqrt(21)]/2 or e^x = [5 - sqrt(21)]/2
Take the natural log of both sides to get:
x = ln[[5 + sqrt(21)]/2] or x = ln[[5 - sqrt(21)]/2]
x = ln[4.79129] or x = ln[208712]
x = 1.5668  or x = -1.5668
=============================
Cheers,
Stan H.