Question

Tìm x: a, \(3\sqrt{x-2}-\sqrt{x^2-4}=0\)
b, \(\left(\sqrt{x+4}-2\right)\left(\sqrt{4-x}+2\right)=-2x\)

Answer 1

Câu a : \(3\sqrt{x-2}-\sqrt{x^2-4}=0\) ( ĐK : \(x\ge2\) )

\(\Leftrightarrow3\sqrt{x-2}-\sqrt{\left(x+2\right)\left(x-2\right)}=0\)

\(\Leftrightarrow\sqrt{x-2}\left(3-\sqrt{x+2}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-2}=0\\3-\sqrt{x+2}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\left(TM\right)\\x=7\left(TM\right)\end{matrix}\right.\)

Vậy \(x=2\) hoặc \(x=7\)