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Quadratics
Review question
If $2y = a^x + a^{-x}$, can we find $a^x$?
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Ref: R6816
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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
\[\begin{equation*} z = 4y^3 - 3y. \end{equation*}\]
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