Đáp án:
C4:
\(\left\{ \begin{array}{l}
a < \dfrac{1}{3}\\
a \ne - \dfrac{1}{{21}}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
C3:\\
Xét:{x^2} - x - 2 = 0\\
\to \left( {x - 2} \right)\left( {x + 1} \right) = 0\\
\to \left[ \begin{array}{l}
x = 2\\
x = - 1
\end{array} \right.\\
Do:f\left( x \right) \vdots {x^2} - x - 2
\end{array}\)
⇒ x=2 và x=-1 là nghiệm của f(x)
\(\begin{array}{l}
\to \left\{ \begin{array}{l}
f\left( { - 1} \right) = 0\\
f\left( 2 \right) = 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
1 + 9 + 21 - a + b = 0\\
16 - 72 + 84a + b = 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
a = \dfrac{{87}}{{85}}\\
b = - \dfrac{{2548}}{{85}}
\end{array} \right.
\end{array}\)
\(\begin{array}{l}
C4:\\
DK:x \ne - 7\\
\to \dfrac{{1 - 21a}}{{1 - 3a}} = x + 7\\
\to x = \dfrac{{1 - 21a}}{{1 - 3a}} - 7 = \dfrac{{1 - 21a - 7 + 21a}}{{1 - 3a}}\\
= \dfrac{{ - 6}}{{1 - 3a}} = \dfrac{6}{{3a - 1}}\\
Do:x < 0;x \ne - 7\\
\to \left\{ \begin{array}{l}
\dfrac{6}{{3a - 1}} < 0\\
\dfrac{6}{{3a - 1}} \ne - 7
\end{array} \right.\\
\to \left\{ \begin{array}{l}
3a - 1 < 0\\
6 \ne 21a + 7
\end{array} \right.\\
\to \left\{ \begin{array}{l}
a < \dfrac{1}{3}\\
a \ne - \dfrac{1}{{21}}
\end{array} \right.
\end{array}\)
