Using the definition of \(\cosh x\) in terms of \(\mathrm { e } ^ { x }\) and \(\mathrm { e } ^ { - x }\), show that
$$4 \cosh ^ { 3 } x - 3 \cosh x \equiv \cosh 3 x$$
Use the substitution \(u = \cosh x\) to find, in terms of \(5 ^ { \frac { 1 } { 3 } }\), the real root of the equation
$$20 u ^ { 3 } - 15 u - 13 = 0 .$$