e^x + e^-x = 4
e^x + 1/e^x =4
Let y=e^x
then y + 1/y = 4
multiply by y
y^2 +1 = 4y
y^2 -4y +1 = 0
use the quadratic formula or complete the square
y = 4/2 + or - (1/2)sqr(16-4)
y = 2 + or - .5sqr12
y =2 + or - sqr3 = e^x
take natural logs of both sides
ln|2+ or - sqr3| = x
x = approximately ln|3.732| or ln|0.268|
use a calculator with a natural log function
x = about 1.317 or -1.317
check the answer
e^1.317+ 1/e^1.317
= about 3.732 + .268 = 4
