Solve for x: e^x + e^-x = 3. Please explain what kind of property or steps you took to get your answer.?

Question

To help you out: x is about .96 and -.96.

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Answer 1

e^x + e^-x = 3

Multiply throughout by e^x

e^2x + 1 = 3e^x

e^2x - 3e^x + 1 = 0

Treat the last line as a quadratic in e^x

y^2 - 3y + 1 = 0 with y = e^x

Using quadratic formula

y = (3 +/-sqrt(5))/2

e^x = (3 +/- sqrt(5))/2

x = ln(3 +/- sqrt(5)) - ln2