ĐKXĐ:\(x-3\ge0\Rightarrow x\ge3\)
\(x-2\sqrt{x-3}=3\\ \Rightarrow x-3=2\sqrt{x-3}\\ \Rightarrow x^2-6x+9=4x-12\\ \Rightarrow x^2-10x+21=0\\ \Rightarrow\left(x-3\right)\left(x-7\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=7\left(tm\right)\end{matrix}\right.\)
x−2√x−3=3(ĐK:x≥3)x-2x-3=3(ĐK:x≥3)
⇔2√x−3=x−3⇔2x-3=x-3
⇔√x−3(√x−3−2)=0⇔x-3(x-3-2)=0
⇔√x−3=0⇔x-3=0 hoặc √x−3=2x-3=2
⇔x−3=0⇔x-3=0 hoặc x−3=4x-3=4
⇔x=3⇔x=3 hoặc x=7
ĐK : \(x\ge3\)
pt \(\Leftrightarrow2\sqrt{x-3}=x-3\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge3\\4\left(x-3\right)=x^2-6x+9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge3\\x^2-10x+21=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge3\\\left[{}\begin{matrix}x=7\\x=3\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=7\\x=3\end{matrix}\right.\)
