Đặt $y_1=x+2\sqrt{3x}$
$\sqrt{x+2\sqrt{x+2\sqrt{x+...+2\sqrt{x+2\sqrt{3x}}}}}=x\Leftrightarrow \left\{\begin{matrix}y_1=x+2\sqrt{3x}\\y_2=x+2\sqrt{y_1}\\...\\y_{n-1}=x+2\sqrt{y_{n-2}}\\y_n=x+2\sqrt{y_{n-1}}=3x \end{matrix}\right.\Leftrightarrow\left \{\begin{matrix}y_1=y_2=...=y_{n-1}=y_n=3x \\3x=x+2\sqrt{3x}\end{matrix}\right.\Leftrightarrow \left[\begin{matrix}x=0\\ x=3\end{matrix}\right.$
Bạn ơi giải thích giúp mình với $y_{1}=y_{2}=...=y_{n}$