Question

[Miessi Xám]

cho 3 số a,b,c thỏa mãn a+b+c=0 . hãy so sánh 3 số . A= a(a+b)(c+a)

B=b(b+c)(a+b)            .            C= c(c+a)(b+c)

Answer 1

[Nguyễn Việt Lâm]

\(a+b+c=0\Rightarrow\left\{{}\begin{matrix}a+b=-c\\c+a=-b\\b+c=-a\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}A=a.\left(-c\right).\left(-b\right)=abc\\B=b.\left(-a\right).\left(-c\right)=abc\\C=c.\left(-b\right).\left(-a\right)=abc\end{matrix}\right.\)

\(\Rightarrow A=B=C\)