Question

giải phương trình 
\(\sqrt{x^2-16}-3\sqrt{x+4}=0\)

Answer 1

\(\Leftrightarrow\sqrt{x+4}\left(\sqrt{x-4}-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x-4=9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=13\end{matrix}\right.\)

Answer 2

ĐKXĐ: \(\left[{}\begin{matrix}x\ge4\\x=-4\end{matrix}\right.\)

\(pt\Leftrightarrow\sqrt{\left(x-4\right)\left(x+4\right)}-3\sqrt{x+4}=0\)

\(\Leftrightarrow\sqrt{x+4}.\left(\sqrt{x-4}-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+4}=0\\\sqrt{x-4}=3\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\x-4=9\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-4\left(tm\right)\\x=13\left(tm\right)\end{matrix}\right.\)

Answer 3

ĐKXĐ: \(\left[{}\begin{matrix}x\ge4\\x=-4\end{matrix}\right.\)

\(\Leftrightarrow\sqrt{\left(x-4\right)\left(x+4\right)}=3\sqrt{\left(x+4\right)}\\ \Leftrightarrow\left(x-4\right)\left(x+4\right)=9\left(x+4\right)\\ \Leftrightarrow\left(x+4\right)\left(x-13\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-4\left(tm\right)\\x=13\left(tm\right)\end{matrix}\right.\)