Question

Tìm x biết x² > 4

Answer 1

\(x^2>4\)

\(\Leftrightarrow x^2>\left(\pm2\right)^2\)

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

Answer 2

Cảm ơn Nguyen Thi Huyen mình nhớ ra cách giải rồi

\(x^2>4\)

\(x^2-4>0\)

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

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

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

Vậy (x - 2)(x + 2) > 0 khi x > 2; x < -2 hay x² > 4 khi x > 2; x < -2