Question

Giải phương trình sau:

\(\left(x-3\right)\sqrt{x^2-4}=x^2-9\)

Answer 1

\(\left(x-3\right)\sqrt{x^2-4}=x^2-9\) (ĐK: \(\left\{{}\begin{matrix}x< -2\\x\ge2\end{matrix}\right.\)) 

\(\Leftrightarrow\left(x-3\right)\sqrt{x^2-4}=\left(x-3\right)\left(x+3\right)\)

\(\Leftrightarrow\sqrt{x^2-4}=\dfrac{\left(x-3\right)\left(x+3\right)}{x-3}\)

\(\Leftrightarrow\sqrt{x^2-4}=x+3\)

\(\Leftrightarrow x^2-4=\left(x+3\right)^2\)

\(\Leftrightarrow x^2-4=x^2+6x+9\)

\(\Leftrightarrow x^2-x^2-6x=9+4\)

\(\Leftrightarrow-6x=13\)

\(\Leftrightarrow x=-\dfrac{13}{6}\left(tm\right)\)

Vậy: ...