If $2y = a^x + a^{-x}$, can we find $a^x$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource
Given that $2y = a^x + a^{-x}$, where $a > 1$, $x > 0$, prove that $\begin{equation*} a^x = y + \sqrt{y^2-1}. \end{equation*}$ If, further, $2z = a^{3x} + a^{-3x}$, prove that $\begin{equation*} z = 4y^3 - 3y. \end{equation*}$