\(a+b+c=0\Rightarrow\left\{{}\begin{matrix}a+b=-c\\a+c=-b\\b+c=-a\end{matrix}\right.\)
\(\Rightarrow a.\left(-c\right).\left(-b\right)=b.\left(-a\right).\left(-c\right)\)
\(\Rightarrow a.b.c=a.b.c\) ( luôn đúng )
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Ta có:
\(a+b+c=0\Rightarrow\left\{{}\begin{matrix}a+b=-c\\b+c=-a\\a+c=-b\end{matrix}\right.\)
⇒ a.(a+b).(a+c)=b.(b+c).(b+a)
\(\Rightarrow\) a.(−c).(−b)=b.(−a).(−c)
⇒a.b.c=a.b.c
Vậy khi a+b+c = 0 thì : a.(a+b).(a+c)=b.(b+c).(b+a)
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