exponential equation

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Solve the exponential equation
e^x + e^-x = 6

  • exponential equation -

    let 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..

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