a) \(x+\sqrt{x}=6\left(x\ge0\right)\)
\(\Leftrightarrow x+\sqrt{x}-6=0\)
\(\Leftrightarrow\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)=0\)
\(\Leftrightarrow\sqrt{x}-2=0\)
\(\Leftrightarrow\sqrt{x}=2\)
\(\Leftrightarrow x=4\)(tm)
b) \(\sqrt{x^2+2x+4}=x-1\) (ĐK: \(x\ge1\))
\(\Leftrightarrow x^2+2x+4=\left(x-1\right)^2\)
\(\Leftrightarrow x^2+2x+4=x^2-2x+1\)
\(\Leftrightarrow4x+3=0\)
\(\Leftrightarrow4x=-3\)
\(\Leftrightarrow x=-\dfrac{3}{4}\) (ktm)
c) \(x^2-3x+3\sqrt{x^2-3x-3}=7\)
\(\Leftrightarrow x^2-3x-3+3\sqrt{x^2-3x-3}-4=0\)
Đặt: \(t=\sqrt{x^2-3x-3}\) \(\left(t\ge0\right)\)
\(\Leftrightarrow t^2+3t-4=0\)
\(\Leftrightarrow\left(t+4\right)\left(t-1\right)=0\)
\(\Leftrightarrow t=1\)
\(\Leftrightarrow\sqrt{x^2-3x-3}=1\)
\(\Leftrightarrow x^2-3x-4=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=4\end{matrix}\right.\)
