Question

cho a+b+c=0

cmr M=N=P biết

M=a(a+b)(a+c)

N=b(b+c)(b+a)

P=c(c+a)(c+b)

Answer 1

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

\(\Rightarrow\left\{{}\begin{matrix}M=a\left(a+b\right)\left(a+c\right)=a.\left(-c\right).\left(-b\right)=abc\\N=b\left(b+c\right)\left(b+a\right)=b.\left(-a\right).\left(-c\right)=abc\\P=c\left(c+a\right)\left(c+b\right)=c.\left(-b\right).\left(-a\right)=abc\end{matrix}\right.\)

Vậy \(M=N=P\) ( đpcm )

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