Question

giải phương trình: \(\sqrt{x^2-9}+6=3\sqrt{x+3}+2\sqrt{x-3}\)

Answer 1

ĐKXĐ: ...

Đặt \(\left\{{}\begin{matrix}\sqrt{x+3}=a\\\sqrt{x-3}=b\end{matrix}\right.\)

\(\Rightarrow ab+6=3a+2b\)

\(\Leftrightarrow ab-3a-2b+6=0\)

\(\Leftrightarrow a\left(b-3\right)-2\left(b-3\right)=0\)

\(\Leftrightarrow\left(a-2\right)\left(b-3\right)=0\Rightarrow\left[{}\begin{matrix}a=2\\b=3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\sqrt{x+3}=2\\\sqrt{x-3}=3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=1\\x=12\end{matrix}\right.\)