`@` `10MN`

`3x^2 +8y^2 + 23z^2 + 6xy-22yz-12zx-12z+ 6=0`

`<=>3x^2+3y^2+5y^2+12z^2+5z^2+6z^2+6xy-12yz-10yz-12xz-12z+6=0`

`<=>(3x^2+3y^2+12z^2+6xy-12yz-12xz)+(5y^2-10yz+5z^2)+(6z^2-12z+6)=0`

`<=>3(x^2+y^2+4z^2+2xy-4yz-4xz)+5(y^2-2yz+z^2)+6(z^2-2z+1)=0`

`<=>3(x+y-2z)^2+5(y-z)^2+6(z-1)^2=0`

`<=>` `{((x+y-2z)^2=0),((y-z)^2=0),((z-1)^2=0):}`

`<=>` `{(x+y-2=0),(y-1=0),(z=1):}`

`<=>` `{(x+1-2=0),(y=1),(z=1):}`

`<=>` `{(x=1),(y=1),(z=1):}`

Vậy `x=1;y=1;z=1`