Đáp án:$M = 2$
Giải thích các bước giải:
$\begin{array}{l}
7{x^2} - 2x - 3 = 0\\
Theo\,Viet:\left\{ \begin{array}{l}
{x_1} + {x_2} = \dfrac{2}{7}\\
{x_1}{x_2} = - \dfrac{3}{7}
\end{array} \right.\\
\left\{ \begin{array}{l}
7x_1^2 - 2{x_1} - 3 = 0\\
7x_2^2 - 2{x_2} - 3 = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
7x_1^2 - 2{x_1} = 3\\
7x_2^2 - 2{x_2} = 3
\end{array} \right.\\
M = \dfrac{{7x_1^2 - 2{x_1}}}{3} + \dfrac{3}{{7x_2^2 - 2{x_2}}}\\
= \dfrac{3}{3} + \dfrac{3}{3}\\
= 2
\end{array}$