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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 $abcd$.

 Aug 29, 2020
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abcd = 47.

 Aug 29, 2020

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