$9x^{2}+$ $y^{2}+$ $2z^{2}+18+4z-6y+20=0$
$\text{ ⇒ [ ( 3x } $$^{2})-2.3x.3+9]+($ $y^{2}-2y.3+9)+(2z$$^{2}+4x+2)=0$
$\text{ ⇒ ( 3x - 3 )}$$^{2}+(y-3)$$^{2}+2($ $z^{2}+2z+1)=0$
$\text{ ⇒ ( 3x - 3 )}$$^{2}+(y-3)$$^{2}+2(z+1)$$^{2}=0$
$\text{ vì ( 3x - 3 )}$$^{2}$ $\geq0 $ $\text{ với mọi x }$
$(y-3^{2})$ $\geq0$ $\text{ với mọi y }$
$2(z+1)^{2}$ $\geq0$ $\text{ với mọi z }$
$\text{ ⇒ ( 3x - 3 )}$$^{2}+(y-3)$$^{2}+2(z+1)$$^{2}$ $\geq0$ $\text{ với mọi x , y , z }$
$\text{ mà ( 3x - 3 ) }$$^{2}+(y-3)$$^{2}+2(z+1)$$^{2}=0$
$⇒\left[\begin{array}{ccc}(3x-3)^{2}=0\\(y-3)^{2}=0\\2(z+1)^{2}=0\end{array}\right]$ $⇒\left[\begin{array}{ccc}3x-3=0\\y-3=0\\(z+1)^{2}=0\end{array}\right]$
$⇒\left[\begin{array}{ccc}3(x-1)=0\\y=3\\z+1=0\end{array}\right]$ $⇒\left[\begin{array}{ccc}x-1=0\\y=3\\z=-1\end{array}\right]$ $⇒\left[\begin{array}{ccc}x=1\\y=3\\z=-1\end{array}\right]$
$\text{ Vậy x = 1 ; y = 3 ; z = -1 }$
