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 $abcd$.

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Soccerhannah98781idn Soccerhannah98781idn

07-03-2022
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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 $abcd$.

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