$\begin{array}{l}
{x^3} - 3{x^2} - 9x + m = 0\\
PT\,co\,3\,nghiem\,phan\,biet\,{x_1},{x_2},{x_3}\,thi:\\
\left\{ \begin{array}{l}
{x_1} + {x_2} + {x_3} = 3\\
{x_1}{x_2} + {x_2}{x_3} + {x_3}{x_1} = - 9\\
{x_1}{x_2}{x_3} = - m
\end{array} \right.\\
Ba\,nghiem\,lap\,thanh\,CSC \Rightarrow 2{x_2} = {x_1} + {x_3}\\
\Rightarrow 3{x_2} = 3 \Leftrightarrow {x_2} = 1\\
Thay\,vao\,pt\,duoc:\\
1 - 3 - 9 + m = 0 \Leftrightarrow m = 11\\
Thu\,lai\,m = 11\,thi\,phuong\,trinh:\\
{x^3} - 3{x^2} - 9x + 11 = 0 \Leftrightarrow \left( {x - 1} \right)\left( {{x^2} - 2x - 11} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 1\\
{x^2} - 2x - 11 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 1\\
x = 1 \pm 2\sqrt 3
\end{array} \right.\\
Ba\,nghiem\,nay\,lap\,thanh\,CSC.\\
Vay\,m = 11
\end{array}$
