Ta có: [tex](x+6)^2\geq 0,(3y-9)^4\geq 0,|x-y-z+3|\geq 0\Rightarrow (x+6)^2+(3y-9)^4+|x-y-z+3|\geq 0[/tex]
Dấu "=" xảy ra khi [tex]\left\{\begin{matrix} x+6=0\\ 3y-9=0\\ x-y-z+3=0 \end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x=-6\\ y=3\\ z=-6 \end{matrix}\right.\Rightarrow x+y+z=-9[/tex]