Question

tìm x,y,z thỏa mãn phương trình

Answer 1

\(9x^2+y^2+2z^2-18x+4y-8z+21=0\)

\(\Leftrightarrow\left(9x^2-18x+9\right)+\left(y^2+4y+4\right)+\left(2z^2-8z+8\right)=0\)

\(\Leftrightarrow9\left(x-1\right)^2+\left(y+2\right)^2+2\left(z-2\right)^2=0\)

\(mà:\left(x-1\right)^2\ge0;\left(y+2\right)^2\ge0;\left(z-2\right)^2\ge0\)

\(\Rightarrow\left\{{}\begin{matrix}\left(x-1\right)^2=0\\\left(y+2\right)^2=0\\\left(z-2\right)^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-2\\z=2\end{matrix}\right.\)