Well, I was a lousy ass during the lessons so I ended up quite rundown by a truck when I checked out the questions.. private lessons turned out to help a great deal, but i'm stuck with this one question that i really can't move past it (i skipped it for the time being but would like getting it solved for once :P)

Solve, for real values of x, the following equation:

$\displaystyle 4 tanh^2 x - sech x = 1$

Trying to open it up using the sinh x and cosh x rules got me a little bit lost in it

$\displaystyle sinh x = \frac{ e^x - e^{-x}}{2}$

and $\displaystyle cosh x = \frac{e^x + e^{-x}}{2}$

Solution to that one would be awesome

One more question my brain cells just won't go past is this one:

Solve, for real values of x, the following equation:

$\displaystyle sinh^2 x - 5 cosh x + 5 = 0$

The powers just confuse me, trying to use the identities led me to

$\displaystyle (cosh 2x -1) - 10 cosh x + 9 = 0$

(...messing a bit around with it...)

$\displaystyle e^{2x} + e^{-2x} - 10e^x + 10e^{-x} + 18 = 0$

And from then onwards, my brain shuts down. I can't get past that =/