The three values of $\displaystyle \cosh x$ given by the equation

$\displaystyle a\cosh 3x+b\cosh 2x=0$

whereaandbare non-zero, are $\displaystyle y_1$, $\displaystyle y_2$, and $\displaystyle y_3$.

Show that $\displaystyle y_1y_2+y_2y_3+y_1y_3$ is independent ofaandb.

$\displaystyle a\cosh 3x+b\cosh 2x=0$

$\displaystyle 4a\cosh^3 x+2b\cosh^2 x-3a\cosh x-b=0$

I need to know the general formula for the roots? Or is there some simpler way?

Thanks!