Find ABC

Algebra Level 3

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

{ab(a+b+c)=1001bc(a+b+c)=2002ca(a+b+c)=3003\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 abcabc

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