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Algebra Level 3

Given the three equations for a,b,cRa,b,c \in R: {b2=aca+b+c=21a2+b2+c2=189\begin{cases} b^2=ac \\a+b+c=21 \\ a^2+b^2+c^2=189 \end{cases} Find a×b×c\large \lfloor a \times b \times c \rfloor.

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