Question

a) (x+2).(x-5) > 0

b) (x-3).(x+4) < 0

Answer 1

a)\(\left(x+2\right)\left(x-5\right)>0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+2>0\\x-5>0\end{matrix}\right.\\\left\{{}\begin{matrix}x+2< 0\\x-5< 0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>-2\\x>5\end{matrix}\right.\\\left\{{}\begin{matrix}x< -2\\x< 5\end{matrix}\right.\end{matrix}\right.\)

Vậy \(x>5\) hoặc \(x< -2\)

b) \(\left(x-3\right)\left(x+4\right)< 0\)

Với mọi \(x\in R\) ta có: \(x+4>x-3\)

\(\Rightarrow\left\{{}\begin{matrix}x+4>0\\x-3< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>-4\\x< 3\end{matrix}\right.\)

\(\Rightarrow-4< x< 3\)