Question

Tìm x,y,z thoả mãn phương trình sau:

9x² + y² + 2z² -18x+ 4z - 6y + 20 = 0

Answer 1

\(9x^2+y^2+2z^2-18x+4z-6y+20=0\)

\(\left(9x^2-18x+9\right)+\left(y^2-6y+9\right)+\left(2z^2+4z+2\right)=0\)

\(\Leftrightarrow\left(3x-3\right)^2+\left(y-2\right)^2+\left(\sqrt{2}z+\sqrt{2}\right)^2=0\)

Vì: \(\left(3x-3\right)^2+\left(y-2\right)^2+\left(\sqrt{2}z+\sqrt{2}\right)^2\ge0\forall x,y,z\)

=> Dấu = xảy ra khi: \(\left\{{}\begin{matrix}3x-3=0\\y-2=0\\\sqrt{2}z+\sqrt{2}=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2\\z=-1\end{matrix}\right.\)

Vậy.................