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# Let a, b, c, and d be distinct real numbers such that...

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Let a, b, c, and d be distinct real numbers such that

\begin{align*} a &= \sqrt{4 + \sqrt{5 + a}}, \\ b &= \sqrt{4 - \sqrt{5 + b}}, \\ c &= \sqrt{4 + \sqrt{5 - c}}, \\ d &= \sqrt{4 - \sqrt{5 - d}}. \end{align*}

Compute abcd.

Nov 27, 2018
edited by CrystalRead  Nov 28, 2018