Problem

(a) Use the definition of $\cosh x$ in terms of exponentials to show that

$$2\cosh 5x \cosh x = \cosh 6x + \cosh 4x$$

(b) Hence determine the exact values of $x$ for which

$$\cosh 6x + \cosh 4x = 8\cosh x$$

giving your answers in terms of natural logarithms in simplest form.