\(\sqrt{x}=x\)
\(\Rightarrow x-\sqrt{x}=0\)
\(\Rightarrow\sqrt{x}\left(\sqrt{x}-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{x}=0\\\sqrt{x}-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\end{matrix}\right.\)
\(x-2\sqrt{x}=0\)
\(\Rightarrow\sqrt{x}\left(\sqrt{x}-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{x}=0\\\sqrt{x}-2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\\left[{}\begin{matrix}x=\sqrt{2}\\x=-\sqrt{2}\end{matrix}\right.\end{matrix}\right.\)
\(\sqrt{x+1}=1-x\)
\(\Rightarrow\left|x+1\right|=1-2x+x^2\)
Với \(x\ge-1\) ta có:
\(x+1=1-2x+x^2\)
\(\Rightarrow x+1-1+2x-x^2=0\)
\(\Rightarrow3x-x^2=0\)
\(\Rightarrow x\left(3-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\3-x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
Với \(x< -1\) ta có:
\(-x-1=1-2x+x^2\)
\(\Rightarrow1-2x+x^2+x-1=0\)
\(\Rightarrow3x+x^2=0\)
\(\Rightarrow x\left(3+x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\3+x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-3\end{matrix}\right.\)
Còn pt vô tỉ tui chưa học
