ĐKXĐ : \(x\ge-2\)
\(\sqrt{x^2-4}-\sqrt{x+2}=0\)
\(\Leftrightarrow\sqrt{x-2}.\sqrt{x+2}-\sqrt{x+2}=0\)
\(\Leftrightarrow\sqrt{x+2}\left(\sqrt{x-2}-1\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}\sqrt{x+2}=0\\\sqrt{x-2}-1=0\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=-2\\x=3\end{array}\right.\) (TMĐK)
Vậy tập nghiệm của pt có 2 phần tử
\(\sqrt{x^2-4}-\sqrt{x+2}=0\left(ĐK:x\ge-2\right)\)
\(\Leftrightarrow\sqrt{x^2-4}=\sqrt{x+2}\)
\(\Leftrightarrow x^2-4=x+2\)
\(\Leftrightarrow x^2-x-6=0\)
\(\Leftrightarrow x^2+2x-3x-6=0\)
\(\Leftrightarrow x\left(x+2\right)-3\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x+2=0\\x-3=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=-2\\x=3\end{array}\right.\)
