Question

Giải phương trình

\(\sqrt{3x+7}-\sqrt{x+1}=2\)

Answer 1

ĐK: \(x\ge-1\)

\(\sqrt{2x+7}-\sqrt{x+1}=2\)

\(\Leftrightarrow\sqrt{2x+7}=2+\sqrt{x+1}\)

\(\Leftrightarrow3x+7=4+4\sqrt{x+1}+x+1\)

\(\Leftrightarrow x+1=2\sqrt{x+1}\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+1\right)^2=4\left(x+1\right)\\x+1\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2-2x-3=0\\x\ge-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-1\left(tm\right)\end{matrix}\right.\)