Từ xy+yz+zx=0 => 2(xy+yz+zx)=0
Từ x+y+z=0 => (x+y+z)2=0
=>x2+y2+z2+2(xy+yz+zx)=0
=>x2+y2+z2=0
Mà \(x^2\ge0,y^2\ge0,z^2\ge0\Rightarrow x^2+y^2+z^2\ge0\)
=>x=y=z=0
Thay x=y=z=0 vào A
=>A=-1+1-1=-1
\(x+y+z=0\)
\(\Leftrightarrow\)\(\left(x+y+z\right)^2=0\)
\(\Leftrightarrow\)\(x^2+y^2+z^2+2xy+2yz+2zx=0\)
\(\Leftrightarrow\)\(x^2+y^2+z^2+2\left(xy+yz+zx\right)=0\)
\(\Leftrightarrow\)\(x^2+y^2+z^2=0\)
\(\Leftrightarrow\)\(\hept{\begin{cases}x^2=0\\y^2=0\\z^2=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=0\\y=0\\z=0\end{cases}\Leftrightarrow}x=y=z=0}\)
\(\Rightarrow\)\(A=\left(x-1\right)^{2015}+y^{2016}+\left(z+1\right)^{2017}=\left(-1\right)^{2015}+0^{2016}+1^{2017}=-1+0+1=2\)
Vậy \(A=2\)
Chúc bạn học tốt ~
