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a =\sqrt{45-\sqrt{21-a}}, b =\sqrt{45+\sqrt{21-b}}, c =\sqrt{45-\sqrt{21+c}},

Source: Switzerland - Swiss TST 2004 p7

February 18, 2020
system of equationsProductalgebra

Problem Statement

The real numbers a,b,c,da,b,c,d satisfy the equations: {a=45−21−ab=45+21−bc=45−21+c d=45+21+d\begin{cases} 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 {cases} Prove that abcd=2004abcd = 2004.
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