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October 22, 2016
Posted by **Tiffany** on Sunday, April 7, 2013 at 11:47pm.

e^x + e^-x = 6

- exponential equation -
**Reiny**, Monday, April 8, 2013 at 12:00amlet e^x = a

then we have

a + 1/a = 6

a^2 + 1 - 6a = 0

a^2 - 6a = -1

completing the square, (in this case faster than using the formula)

a^2 - 6a + 9 = -1 + 9

(a-3)^2 = 8

a-3 = ± √8

a = 3± 2√2

so e^x = 3 + √8 OR e^x = 3 - √8

using my calculator

x = ln(3+√8) = 1.7627.. or

x = ln(3-√8) = -1.7627..