Question

bài 1

a/  \(\sqrt{x^2+6x+9}\) = 3x - 6

Answer 1

\(\sqrt{x^2+6x+9}=3x-6\\ \Leftrightarrow\sqrt{\left(x+3\right)^2}=3x-6\\ \Leftrightarrow\left|x+3\right|=3x-6\)

Nếu \(\left\{{}\begin{matrix}x+3\ge0\Leftrightarrow x\ge-3\\x+3< 0\Leftrightarrow x< -3\end{matrix}\right.\)

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