\(x+y+z=0\\ \Leftrightarrow\left\{{}\begin{matrix}x+y=-z\\y+z=-x\\x+z=-y\end{matrix}\right.\\ M=\left(x+y\right)\left(y+z\right)\left(x+z\right)\\ =\left(-z\right).\left(-x\right).\left(-y\right)\\ =-\left(xyz\right)=-1.\left(2\right)=-2\)
Ta có :
\(x+y+z=0\Rightarrow\left\{{}\begin{matrix}x+y=-z\\y+z=-x\\x+z=-y\end{matrix}\right.\)
Thay vào biểu thức \(M\) ta được :
\(M=\left(-z\right).\left(-x\right).\left(-y\right)=-\left(zxy\right)=-2\)
( Do \(xyz=2\) )
Vậy : \(M=-2\)
\(x+y+z=0\Leftrightarrow\left\{{}\begin{matrix}x=-\left(y+z\right)\\y=-\left(x+z\right)\\z=-\left(x+y\right)\end{matrix}\right.\)
Nhân theo vế: \(xyz=-\left(x+y\right).\left(y+z\right).\left(x+z\right)\)
\(\Rightarrow2=-\left(x+y\right).\left(y+z\right).\left(x+z\right)\)
\(\Rightarrow M=\left(x+y\right).\left(y+z\right).\left(x+z\right)=-2.\)
Vậy \(M=-2.\)
Chúc bạn học tốt!
