Đáp án:
a) \(\left[ \begin{array}{l}
x = 0\\
x = 8
\end{array} \right.\)
b) \(\left[ \begin{array}{l}
m = 11\\
m = - 3\\
m = 5\\
m = 3
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
3)a)Thay:m = 4\\
Pt \to {x^2} - 8x = 0\\
\to x\left( {x - 8} \right) = 0\\
\to \left[ \begin{array}{l}
x = 0\\
x = 8
\end{array} \right.\\
b)Xét:\Delta ' \ge 0\\
\to {m^2} - m + 4 \ge 0\left( {ld} \right)\forall m\\
Vi - et:\left\{ \begin{array}{l}
{x_1} + {x_2} = 2m\\
{x_1}{x_2} = m - 4
\end{array} \right.\\
A = \dfrac{{{x_1} + {x_2} - 1}}{{{x_1}{x_2}}} = \dfrac{{2m - 1}}{{m - 4}}\\
= \dfrac{{2\left( {m - 4} \right) + 7}}{{m - 4}}\\
= 2 + \dfrac{7}{{m - 4}}\\
A \in Z \to \dfrac{7}{{m - 4}} \in Z\\
\to m - 4 \in U\left( 7 \right)\\
\to \left[ \begin{array}{l}
m - 4 = 7\\
m - 4 = - 7\\
m - 4 = 1\\
m - 4 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
m = 11\\
m = - 3\\
m = 5\\
m = 3
\end{array} \right.
\end{array}\)
