$4x^2+2y^2+2z^2-4xy-2xz+2yz-6y-10z+34=0$$\Leftrightarrow (4x^2+y^2+z^2-4xy-4xz+2xz)+(y^2-6y+9)+(z^2-10z+25)=0\Leftrightarrow (2x-y-z)^2+(y-3)^2+(z-5)^2=0$$\Leftrightarrow \begin{cases}2x-y-z=0\\y-3=0\\ z-5=0 \end{cases}\Leftrightarrow \begin{cases}x=4 \\z=5\\ y= 3\end{cases}$$\Rightarrow A=0^{22}+(-1)^6+1^{2015}=0$
$4x^2+2y^2+2z^2-4xy-2xz+2yz-6y-10z+34=0$$\Leftrightarrow (4x^2+y^2+z^2-4xy-4xz+2xz)+(y^2-6y+9)+(z^2-10z+25)=0\Leftrightarrow (2x-y-z)^2+(y-3)^2+(z-5)^2=0$$\Leftrightarrow \begin{cases}2x-y-z=0\\y-3=0\\ z-5=0 \end{cases}\Leftrightarrow \begin{cases}x=4 \\z=5\\ y= 3\end{cases}$\Rightarrow $A=0^{22}+(-1)^6+1^{2015}=0$
$4x^2+2y^2+2z^2-4xy-2xz+2yz-6y-10z+34=0$$\Leftrightarrow (4x^2+y^2+z^2-4xy-4xz+2xz)+(y^2-6y+9)+(z^2-10z+25)=0\Leftrightarrow (2x-y-z)^2+(y-3)^2+(z-5)^2=0$$\Leftrightarrow \begin{cases}2x-y-z=0\\y-3=0\\ z-5=0 \end{cases}\Leftrightarrow \begin{cases}x=4 \\z=5\\ y= 3\end{cases}$
$\Rightarrow A=0^{22}+(-1)^6+1^{2015}=0$