Question 128
The equations apply to the real numbers $a$, $b$, $c$, $d$
$$
\begin{array}{ll}
a=\sqrt{45-\sqrt{21-a}}, & b=\sqrt{45+\sqrt{21-b}} \\
c=\sqrt{45-\sqrt{21+c}}, & d=\sqrt{45+\sqrt{21+d}}
\end{array}
$$
Show that $a b c d=2004$ holds.
$$
\begin{array}{ll}
a=\sqrt{45-\sqrt{21-a}}, & b=\sqrt{45+\sqrt{21-b}} \\
c=\sqrt{45-\sqrt{21+c}}, & d=\sqrt{45+\sqrt{21+d}}
\end{array}
$$
Show that $a b c d=2004$ holds.