b, \(mx^2+\left(m-1\right)x+m-1< 0\) và \(x\in R\)
thì \(mx^2+\left(m-1\right)+m+1>0\) với mọi x
\(\Leftrightarrow\left\{{}\begin{matrix}m>0\\\left(m-1\right)^2-4m\left(m-1\right)>0\left(\Delta< 0\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m>0\\m^2-2m+1-4m^2+4m>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m>0\\-3m^2+2m+1>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m>0\\m\in\left\{-\infty,-\dfrac{1}{3}\right\}V\left\{1,+\infty\right\}\end{matrix}\right.\)
=> \(m>-\dfrac{1}{3}\)
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