Toán Lớp 8: tìm m để phương trình sau có nghiệm âm
(m+1)/(x+1)=m^2+3m+2
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Toán Lớp 8: tìm m để phương trình sau có nghiệm âm
(m+1)/(x+1)=m^2+3m+2
Comments ( 1 )
m > – 1\\
m < – 2
\end{array} \right.\)
DK:x \ne – 1\\
\dfrac{{m + 1}}{{x + 1}} = {m^2} + 3m + 2\\
\to x + 1 = \dfrac{{m + 1}}{{\left( {m + 2} \right)\left( {m + 1} \right)}}\left( {m \ne \left\{ { – 2; – 1} \right\}} \right)\\
\to x + 1 = \dfrac{1}{{m + 2}}\\
\to x = \dfrac{1}{{m + 2}} – 1\\
\to x = \dfrac{{1 – m – 2}}{{m + 2}}\\
\to x = \dfrac{{ – 1 – m}}{{m + 2}}
\end{array}\)
\Leftrightarrow \left\{ \begin{array}{l}
\dfrac{{ – 1 – m}}{{m + 2}} < 0\\
\dfrac{{ – 1 – m}}{{m + 2}} \ne – 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\left[ \begin{array}{l}
\left\{ \begin{array}{l}
– 1 – m < 0\\
m + 2 > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
– 1 – m > 0\\
m + 2 < 0
\end{array} \right.
\end{array} \right.\\
– 1 – m \ne – m – 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\left[ \begin{array}{l}
\left\{ \begin{array}{l}
m > – 1\\
m > – 2
\end{array} \right.\\
\left\{ \begin{array}{l}
m < – 1\\
m < – 2
\end{array} \right.
\end{array} \right.\\
– 1 \ne – 2
\end{array} \right.\\
\to \left[ \begin{array}{l}
m > – 1\\
m < – 2
\end{array} \right.
\end{array}\)