đk: x≤-3; x≥3
\(\sqrt{x^2-9}-\sqrt{x+3}=0\)
\(\Leftrightarrow\sqrt{\left(x-3\right)\left(x+3\right)}-\sqrt{x+3}=0\)
\(\Leftrightarrow\sqrt{x+3}\left(\sqrt{x-3}-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+3}=0\\\sqrt{x-3}-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\x-3=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=4\end{matrix}\right.\)(t/m)
vậy.....
Đkxđ: \(x\ge3;x\ge-3\)
\(\Leftrightarrow\sqrt{x+3}\left(\sqrt{x-3}-1\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}\sqrt{x+3}=0\\\sqrt{x-3}-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+3=0\\\sqrt{x-3}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\\x=4\end{matrix}\right.\)
Vậy s={-3;4}
\(\sqrt{x^2-9}-\sqrt{x+3}=0\) ( x ≥ -3 hoặc x ≥ 3 )
⇔ \(\sqrt{x-3}\left(\sqrt{x+3}-1\right)=0\)
⇔ \(x=3\left(TM\right)orx=-2\left(TM\right)\)
KL..........
Đk: \(\left\{{}\begin{matrix}\left[{}\begin{matrix}x\ge3\\x\le-3\end{matrix}\right.\\x\ge-3\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x\ge3\\x=-3\end{matrix}\right.\)
\(\Leftrightarrow\sqrt{x^2-9}=\sqrt{x+3}\Leftrightarrow x^2-9=x+3\Leftrightarrow\left(x+3\right)\left(x-4\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-3\left(N\right)\\x=4\left(N\right)\end{matrix}\right.\)
Kl: x=4, x=-3
