Điều kiện bạn tự làm
\(x+y+z+11=2\sqrt{x}+4\sqrt{y-1}+6\sqrt{z-2}\)
\(\Leftrightarrow\left(x-2\sqrt{x}+1\right)+\left(y-1-4\sqrt{y-1}+4\right)+\left(z-2-6\sqrt{z-2}+9\right)=0\)
\(\Leftrightarrow\left(\sqrt{x}-1\right)^2+\left(\sqrt{y-1}-2\right)^2+\left(\sqrt{z-2}-3\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}x=1\\y=5\\z=11\end{cases}}\)