calculus

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solve the inequality

e^x+e^x-x=6

can you show work

  • calculus -

    You don't have an inequality, you have an equation

    Why do you have two terms the same?
    Is there a typo ?

  • calculus -

    I am sorry.
    This is the equation.
    Solve the follow exponential equation
    e^x+e^-x=6

  • calculus -

    e^-x = 1/e^x
    so
    e^x + 1/e^x = 6

    e^2x/e^x + 1/e^x = 6

    (e^2x + 1) = 6 e^x

    let z = e^x
    z^2 + 1 = 6 z
    z^2 - 6 z + 1 = 0

    z = [ 6 +/- sqrt(36 -4) ] /2
    z = 3 +/- .5 sqrt(32)
    z = 3 +/- 2 sqrt 2

    so
    e^x = 5.828 or e^x = .1716
    ln e^x = x = 1.76 or x = -1.76

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