Question

tìm x \(\sqrt{x^2-4}-\sqrt{x-2}=0\)

Answer 1

\(\Leftrightarrow\sqrt{x-2}\left(\sqrt{x+2}-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+2=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\left(nhận\right)\\x=-1\left(loại\right)\end{matrix}\right.\)

Answer 2

`\sqrt{x^2-4}-\sqrt{x-2}=0`     `ĐK: x >= 2`

`<=>\sqrt{(x-2)(x+2)}-\sqrt{x-2}=0`

`<=>\sqrt{x-2}(\sqrt{x+2}-1)=0`

`<=>` $\left[\begin{matrix} \sqrt{x-2}=0\\ \sqrt{x+2}=1\end{matrix}\right.$

`<=>` $\left[\begin{matrix} x-2=0\\ x+2=1\end{matrix}\right.$

`<=>` $\left[\begin{matrix} x=2\text{ (t/m)}\\ x=-1\text{ (ko t/m)}\end{matrix}\right.$

Vậy `S={2}`