# Solve for x to three significant digits?

##
#e^x + e^-x = 2#

##### 1 Answer

Dec 13, 2016

Real solution:

Complex solutions:

#### Explanation:

Let

Then our equation becomes:

#t + 1/t = 2#

Mutliply through by

#0 = t^2-2t+1 = (t-1)^2#

So the only possible value of

Now solve

The unique Real solution is

There are also Complex solutions resulting from Euler's identity:

#e^(ipi) = -1#

Hence:

#e^((2kpi)i) = ((e^(ipi))^2)^k = ((-1)^2)^k = 1^k = 1#

for any integer