Can I find $a$ and $b$ so that $\cosh(ax) - \cosh(bx) = \cosh(cx)$?

Question

I want to find $a$ and $b$ in terms of $c \in \mathbb R$ that satisfy

$$\cosh(ax) - \cosh(bx) = \cosh(cx)$$

How can I? There are no restrictions on $a$ and $b$.

Answer 1

Put $x=0$ to see that such an equation cannot hold.