Question

Giải bpt: x^2 - 4 > 0

Answer 1

\(x^2-2^2>0\)

\(\Rightarrow\left(x-2\right)\left(x+2\right)=0\)

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

Answer 2

\(x^2-4>0\Leftrightarrow\left(x+2\right)\left(x-2\right)>0\)

\(TH1:\left\{{}\begin{matrix}x-2>0\\x+2>0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x>2\\x>-2\end{matrix}\right.\Rightarrow x>2\)

\(TH2:\left\{{}\begin{matrix}x-2< 0\\x+2< 0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x< 2\\x< -2\end{matrix}\right.\Rightarrow x< -2\)

Từ 2 trường hợp: \(\Rightarrow\left[{}\begin{matrix}x>2\\x< -2\end{matrix}\right.\)

Answer 3

\(\left(x-2\right)\left(x+2\right)>0\) nha lộn