Quadratics

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

Ref: R6816

Printable/supporting materials Printable version Fullscreen mode Teacher notes

Question

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 \[\begin{equation*} z = 4y^3 - 3y. \end{equation*}\]

Previous Next

Quadratics

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

Question

Station

Lines

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