Question

[Kang Soo Ae]

CMR: x<√x <=>0<x<1

Answer 1

[Nguyễn Tấn An]

\(x< \sqrt{x}\Leftrightarrow x^2< x\Leftrightarrow x^2-x< 0\Leftrightarrow x\left(x-1\right)< 0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>0\\x-1< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x< 0\\x-1>0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>0\\x< 1\end{matrix}\right.\Leftrightarrow0< x< 1}\\\left\{{}\begin{matrix}x< 0\\x>1\end{matrix}\right.\Leftrightarrow x\in\varnothing}\end{matrix}\right.\)

Answer 2

[cao minh thành]

Ta có: x<\(\sqrt{x}\) ⇌ x²<x (vô lí)

Vậy đề sai