- #1

- 45

- 0

I was doing some work on hyperbolic functions and teaching myself to solve some equations. One of the questions in the book really has me stumped:

Express using exponential definitions of cosh(x) and sinh(x) find the exact solution of:

tanh(x) + sinh(x) = 3

I had a go at solving it and this is how far I got:

2tanh(x) + 2sinh(x) = 6

2(e

^{2x}-1)/(e

^{2x}-1) + e

^{x}- e

^{-x}= 6

e

^{3x}- 4e

^{2x}- 8 - e

^{-x}= 0

e

^{4x}- 4e

^{3x}- 8e

^{x}- 1 = 0

then if y=e

^{x}

y

^{4}- 4y

^{3}- 8y -1 = 0

After this I get stuck. I can't find any factors in order to solve it using factor theorem so I'm guessing I'm going to get some wierd solutions - but the question asks specifically for exact answers?

Would anyone mind please helping me out? (I really hope I haven't made some pathetic little mistake but I really can't see anything...)

Thanks in advance,

Oscar