Find ABC

Algebra Level 3

\(a,\quad b,\quad c\) are real numbers in the following equation system:

\(\begin{cases} ab\left( a+b+c \right) =1001 \\ bc\left( a+b+c \right) =2002 \\ ca\left( a+b+c \right) =3003 \end{cases}\)

Find \(abc\)

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