Question

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

Answer 1

\(\sqrt{x^2-9}-3\sqrt{x-3}=0\\ \Leftrightarrow\sqrt{\left(x-3\right)\left(x+3\right)}-3\sqrt{x-3}=0\\ \Leftrightarrow\sqrt{x-3}\cdot\sqrt{x+3}-3\sqrt{x-3}=0\\ \Leftrightarrow\left(\sqrt{x-3}\right)\left(\sqrt{x+3}-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{x-3}=0\\\sqrt{x+3}-3=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{x-3}=0\\\sqrt{x+3}=3\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+3=9\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=3\\x=6\end{matrix}\right.\)

Answer 2

Sửa đề: \(\sqrt{x^2-9}-3\sqrt{x-3}=0\)

ĐKXĐ: \(\left\{{}\begin{matrix}x^2-9>=0\\x-3>=0\end{matrix}\right.\)

=>x>=3

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

=>\(\sqrt{x-3}\cdot\sqrt{x+3}-3\sqrt{x-3}=0\)

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

=>\(\left[{}\begin{matrix}x-3=0\\x+3=9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\left(nhận\right)\\x=6\left(nhận\right)\end{matrix}\right.\)

Answer 3

ĐKXĐ: x ≥ 3

Phương trình tương đương:

√[(x - 3)(x + 3)] - 3√(x - 3) = 0

⇔ √(x - 3)[√(x + 3) - 3] = 0

⇔ √(x - 3) = 0 hoặc √(x + 3) - 3 = 0

*) √(x - 3) = 0

⇔ x - 3 = 0

⇔ x = 3 (nhận)

*) √(x + 3) - 3 = 0

⇔ √(x + 3) = 3

⇔ x + 3 = 9

⇔ x = 9 - 3

⇔ x = 6 (nhận)

Vậy S = {3; 6}