Be careful, a,b,c0a,b,c\ne0

Algebra Level 3

Let aa, bb, and cc be non-zero real numbers such that {a2+a=b2b2+b=c2c2+c=a2.\begin{cases} \begin{aligned} a^2+a&=b^2 \\b^2+b&=c^2 \\c^2+c&=a^2. \end{aligned} \end{cases} Find the value of (ab)(bc)(ca)(a-b)(b-c)(c-a).

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