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solving e^2x + e^-2x

could anyone explain to me how to solve
4y^2 = e^2x + e^-2x
using the quadratic formula?

trying to prove arc coshx :smile:
Original post by PiliPala
could anyone explain to me how to solve
4y^2 = e^2x + e^-2x
using the quadratic formula?

trying to prove arc coshx :smile:


I suspect you've arrived at that position erroneously.

Starting from

y=cosh⁡xy=\cosh x

we have,

2y=ex+e−x2y = e^x+e^{-x}

I get the impression you attempted to square this; if so, you missed the cross terms.

Instead, rather than squaring, if you now multiply through by e^x, you get a quadratic in e^x. Apply the quadratic formula.

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