a) Đk: \(x\ge0\)
\(\sqrt{x}\left(\sqrt{x}-3\right)+2=0\\ \Rightarrow x-3\sqrt{x}+2=0\\ \Rightarrow\left[{}\begin{matrix}\sqrt{x}=1\\\sqrt{x}=2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\left(TM\right)\\x=4\left(TM\right)\end{matrix}\right.\)
b) ĐK: \(x\ge0;y\ge1;z\ge2\)
\(\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}=\dfrac{1}{2}\left(x+y+z\right)\\ \Rightarrow2\sqrt{x}+2\sqrt{y-1}+2\sqrt{x-2}=x+y+z\\ \Rightarrow\left(x-2\sqrt{x}+1\right)+\left(y-1-2\sqrt{y-1}+1\right)+\left(z-2-2\sqrt{z-2}+1\right)=0\\ \Rightarrow\left(\sqrt{x}-1\right)^2+\left(\sqrt{y-1}-1\right)^2+\left(\sqrt{z-2}-1\right)^2=0\\ \Rightarrow\left\{{}\begin{matrix}\sqrt{x}-1=0\\\sqrt{y-1}-1=0\\\sqrt{z-2}-1=0\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}x=1\\y=2\\z=3\end{matrix}\right.\left(TM\right)\)
