\(x^2+7x+6\)
\(=x^2+7x+\dfrac{49}{4}-\dfrac{25}{4}\)
\(=\left(x^2+7x+\dfrac{49}{4}\right)-\dfrac{25}{4}\)
\(=\left(x+\dfrac{7}{2}\right)^2-\dfrac{25}{4}\)
Để \(\left(x+\dfrac{7}{2}\right)^2-\dfrac{25}{4}< 0\) thì
\(\left(x+\dfrac{7}{2}\right)^2< \dfrac{25}{4}\)
\(\Rightarrow\left|x+\dfrac{7}{2}\right|< \sqrt{\dfrac{25}{4}}=\dfrac{5}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{7}{2}< \dfrac{5}{2}\\x+\dfrac{7}{2}>-\dfrac{5}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x< -1\\x>-6\end{matrix}\right.\)
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