Tìm x biết: \(\sqrt{x^{2}-9}-3 \sqrt{x-3}=0\)

* Hướng dẫn giải

\(\sqrt{x^{2}-9}-3 \sqrt{x-3}=0(1) \)

\(\begin{aligned} &\text { Điều kiện: }\left\{\begin{array}{l} x^{2}-9 \geq 0 \\ x-3 \geq 0 \end{array} \Leftrightarrow\left\{\begin{array}{c} {\left[\begin{array}{c} x \leq-3 \\ x \geq 3 \\ x \geq 3 \end{array}\right.} \end{array} \Leftrightarrow x \geq 3\right.\right.\\ &\text { (1) } \Leftrightarrow \sqrt{(x-3)(x+3)}-3 \sqrt{x-3}=0 \Leftrightarrow \sqrt{x-3} \sqrt{x+3}-3 \sqrt{x-3}=0\\ &\Leftrightarrow \sqrt{x-3}(\sqrt{x+3}-3)=0 \Leftrightarrow\left[\begin{array}{c} \sqrt{x-3}=0 \\ \sqrt{x+3}-3=0 \end{array} \Leftrightarrow\left[\begin{array}{c} x-3=0 \\ \sqrt{x+3}=3 \end{array} \Leftrightarrow\left[\begin{array}{c} x=3 \\ x+3=9 \end{array} \Leftrightarrow\left[\begin{array}{c} x=3 \\ x=6 \end{array}\right.\right.\right.\right. \end{aligned}\)

Chọn đáp án A