Question

[Nguyen Thi Phung]

Giai các hệ bất phương trình sau :

a/ \(\left\{{}\begin{matrix}x^2+x+5< 0\\x^2-6x+1>0\end{matrix}\right.\)

b/ \(\left\{{}\begin{matrix}2x^2+x-6>0\\3x^2-10x+3\ge0\end{matrix}\right.\)

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

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

e/ \(-4\le\dfrac{x^2-2x-7}{x^2+1}\le1\)

f/ \(\left\{{}\begin{matrix}-x^2+4x-7< 0\\x^2-2x-1\ge0\end{matrix}\right.\)

Answer 1

[Lê Anh Duy]

a)

\(\left\{{}\begin{matrix}x^2+x+5< 0\\x^2-6x+1>0\end{matrix}\right.\)

\(\)Ta có

\(x^2+x+5=\left(x^2+x+\dfrac{1}{4}\right)+\dfrac{19}{4}=\left(x+\dfrac{1}{2}\right)^2+\dfrac{19}{4}\ge\dfrac{19}{4}>0\)

=> Bất phương trình đàu tiên sai, hệ bất phương trình sai

b)

\(\left\{{}\begin{matrix}2x^2+x-6>0\\3x^2-10x+3\ge0\end{matrix}\right.\)

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

\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x>2\\x< -3\end{matrix}\right.\\\left[{}\begin{matrix}x\le-\dfrac{1}{3}\\x\ge3\end{matrix}\right.\end{matrix}\right.\)

Answer 2

[Nguyen Thi Phung]

bạn ơi giải giúp mình câu c, e, f giùm mình với ạ .