Question

\(\sqrt{x^2-36}-\sqrt{x-6}=0\)

Answer 1

`sqrt{x^2-36} - sqrt{x-6} =0`

`Đk : x => +-6`

`<=> sqrt{(x-6)(x+6)} -sqrt{x-6} =0`

Đặt `sqrt{x-6} =a (a>=0)`

`=> a*sqrt{x+6} - a =0`

`=> a( sqrt{x+6} -1) =0`

Th1 : `a =0 => sqrt{x-6}=0 => x=6`

Th2` : sqrt{x+6} -1 =0 => x+6 =1 => x = -5`

Answer 2

\(\sqrt{x^2-36}-\sqrt{x-6}\) = 0 

\(\Leftrightarrow\sqrt{\left(x-6\right)\left(x+6\right)}-\sqrt{x-6}=0\)

\(\Leftrightarrow\sqrt{x-6}\left(\sqrt{x+6}-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-6}=0\\\sqrt{x+6}-1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-5\end{matrix}\right.\)