Use the definitions of hyperbolic functions in terms of exponentials to prove that
$$8 \cosh ^ { 4 } x = \cosh 4 x + p \cosh 2 x + q$$
where \(p\) and \(q\) are constants to be determined.
Hence, or otherwise, solve the equation
$$\cosh 4 x - 17 \cosh 2 x + 9 = 0$$
giving your answers in exact simplified form in terms of natural logarithms.