Question

giải phương trình \(\sqrt{9x^2+6x+1}=\sqrt{11-6\sqrt{2}}\)

Answer 1

\(\Leftrightarrow\left|3x+1\right|=3-\sqrt{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}3x+1=3-\sqrt{2}\left(x\ge\dfrac{-1}{3}\right)\\3x+1=\sqrt{2}-3\left(x< \dfrac{-1}{3}\right)\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2-\sqrt{2}}{3}\\\dfrac{\sqrt{2}-4}{3}\end{matrix}\right.\left(TM\right)}\)

Answer 2

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2-\sqrt{2}}{3}\\x=\dfrac{\sqrt{2}-4}{3}\end{matrix}\right.\)