a/ ĐKXĐ:...
\(9x-6\sqrt{x}+1+4x-4\sqrt{x}y+y^2=0\)
\(\Leftrightarrow\left(3\sqrt{x}-1\right)^2+\left(2\sqrt{x}-y\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}3\sqrt{x}-1=0\\2\sqrt{x}-y=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\frac{1}{9}\\y=\frac{2}{3}\end{matrix}\right.\)
b/ ĐKXĐ: ...
\(\Leftrightarrow x-1+4\left(\sqrt{x+3}-2\right)+2\left(\sqrt{3-2x}-1\right)=0\)
\(\Leftrightarrow x-1+\frac{4\left(x-1\right)}{\sqrt{x+3}+2}-\frac{4\left(x-1\right)}{\sqrt{3-2x}+1}=0\)
\(\Leftrightarrow\left(x-1\right)\left(1+\frac{4}{\sqrt{x+3}+2}-\frac{4}{\sqrt{3-2x}+1}\right)=0\)
\(\Rightarrow x=1\)
c/ ĐKXĐ:...
\(\sqrt{x+4}-\sqrt{1-x}=\sqrt{1-2x}\)
\(\Rightarrow x+4+1-x-2\sqrt{\left(x+4\right)\left(1-x\right)}=1-2x\)
\(\Rightarrow\sqrt{\left(x+4\right)\left(1-x\right)}=x+2\) (\(x\ge-2\))
\(\Rightarrow-x^2-3x+4=x^2+4x+4\)
\(\Rightarrow2x^2+7x=0\Rightarrow\left[{}\begin{matrix}x=0\\x=-\frac{7}{2}\left(l\right)\end{matrix}\right.\)
