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