Problem

(a) Use the definitions of hyperbolic functions in terms of exponentials to prove that

$$8\cosh^4x=\cosh4x+p\cosh2x+q$$

where $p$ and $q$ are constants to be determined.

(b) Hence, or otherwise, solve the equation

$$\cosh4x-17\cosh2x+9=0$$

giving your answers in exact simplified form in terms of natural logarithms.