# 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.
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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