Question

Tìm x thuộc Q biết

(x-1)(x-2)<0

Answer 1

- Để (x-1)(x-2)<0

thì: \(\left\{{}\begin{matrix}x-1< 0\\x-2< 0\end{matrix}\right.\) =>\(\left\{{}\begin{matrix}x< 1\\x< 2\end{matrix}\right.\) => x < 2

- Vậy x < 2 và x\(\in\) Q

Answer 2

Để \(\left(x-1\right)\left(x-2\right)< 0\) thì \(\left(x-1\right)\) và \(\left(x-2\right)\) trái dấu

Mà \(\left(x-1\right)>\left(x-2\right)\)

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

Vậy \(x>1\) hoặc \(x< 2\) \(\)

Answer 3

Ta có : \(\left(x-1\right)\left(x-1\right)< 2\)

=> \(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\\x-2< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\\x-2>0\end{matrix}\right.\end{matrix}\right.\) => \(\left[{}\begin{matrix}\left\{{}\begin{matrix}x>1\\x< 2\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\x>2\end{matrix}\right.\end{matrix}\right.\) (vô lý )

=> \(\left\{{}\begin{matrix}x>1\\x< 2\end{matrix}\right.\) => 1<x<2