Question

Giai hệ bất phương trình sau

\(\left\{{}\begin{matrix}x^2+4x+3\ge0\\2x^2-x-10\le0\\2x^2-5x+3>0\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}x^2+4x+3\ge0\\2x^2-x-10\le0\\2x^2-5x+3>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left(x+1\right)\left(x+3\right)\ge0\\\left(x+2\right)\left(2x-5\right)\le0\\\left(2x-3\right)\left(x-1\right)>0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x\ge-1\\x\le-3\end{matrix}\right.\\-2\le x\le\dfrac{5}{2}\\\left[{}\begin{matrix}x< 1\\x>\dfrac{3}{2}\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}-1\le x\le1\\\dfrac{3}{2}\le x\le\dfrac{5}{2}\end{matrix}\right.\)

Answer 2

là vầy bạn giải ra xong giao nghiệm lại.