Đáp án:
\(\left[ \begin{array}{l}
m = 3\\
m = - 2
\end{array} \right.\)
Giải thích các bước giải:
Xét:
\(\begin{array}{l}
\mathop {\lim }\limits_{x \to 7} f\left( x \right) = \mathop {\lim }\limits_{x \to 7} \dfrac{{{x^2} - 8x - 7}}{{x - 7}}\\
= \mathop {\lim }\limits_{x \to 7} \dfrac{{\left( {x - 1} \right)\left( {x - 7} \right)}}{{x - 7}} = \mathop {\lim }\limits_{x \to 7} \left( {x - 1} \right)\\
= 7 - 1 = 6\\
f\left( 7 \right) = {m^2} - m
\end{array}\)
Do hàm số liên tục tại \({x_0} = 7\)
\(\begin{array}{l}
\to \mathop {\lim }\limits_{x \to 7} f\left( x \right) = f\left( 7 \right)\\
\to {m^2} - m = 6\\
\to {m^2} - m - 6 = 0\\
\to \left( {m - 3} \right)\left( {m + 2} \right) = 0\\
\to \left[ \begin{array}{l}
m = 3\\
m = - 2
\end{array} \right.
\end{array}\)
