Saul is solving the equation
$$2 \cosh x + \sinh ^ { 2 } x = 1$$
He writes his steps as follows:
$$\begin{aligned}
2 \cosh x + \sinh ^ { 2 } x & = 1
2 \cosh x + 1 - \cosh ^ { 2 } x & = 1
2 \cosh x - \cosh ^ { 2 } x & = 0
\cosh x \neq 0 \therefore 2 - \cosh x & = 0
\cosh x & = 2
x & = \pm \cosh ^ { - 1 } ( 2 )
\end{aligned}$$
Identify and explain the error in Saul's method.
9
Anna is solving the different equation
g (b) Anna is solving the different equation
$$\sinh ^ { 2 } ( 2 x ) - 2 \cosh ( 2 x ) = 1$$
and finds the correct answers in the form \(x = \frac { 1 } { p } \cosh ^ { - 1 } ( q + \sqrt { r } )\), where \(p , q\) and \(r\) are integers.
Find the possible values of \(p , q\) and \(r\).
Fully justify your answer.