\(\sqrt{3x+7}-\sqrt{x-1}=3\)
Đkxđ:\(\left\{{}\begin{matrix}3x+7\ge0\\x+1\ge0\end{matrix}\right.\rightarrow\left\{{}\begin{matrix}x\ge-\frac{7}{3}\\x\ge-1\end{matrix}\right.\rightarrow x\ge-1\)
\(PT\rightarrow\sqrt{3x+7}=2+\sqrt{x+1}\)
\(\Rightarrow3x+7=\left(2+\sqrt{x+1}\right)^2\)
\(\Rightarrow3x+7=4+4\sqrt{x+1}+x+1\)
\(\Rightarrow2x+2=4\sqrt{x+1}\)
\(\Rightarrow x+1=2\sqrt{x+1}\)
\(\Rightarrow x^2+2x+1=4\left(x+1\right)\)
\(\Rightarrow x^2-2x-3=0\)
\(\Rightarrow x^2-3x+x-3=0\)
\(\Rightarrow\left(x-3\right)\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=3\left(TM\right)\\x=-1\left(TM\right)\end{matrix}\right.\)
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