Question

Giải pt sau :

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

Answer 1

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

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\\sqrt{x^2+4}=x+3\left(1\right)\end{matrix}\right.\)

Xét (1)

\(\Leftrightarrow\left\{{}\begin{matrix}x+3\ge0\\x^2+4=\left(x+3\right)^2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x\ge-3\\x^2+4=x^2+6x+9\end{matrix}\right.\)

\(\Rightarrow x=-\frac{5}{6}\)