Question

[Minh Tâm]

Chứng minh rằng nếu 0<x<1 thì \(\sqrt{a}>a\)

Answer 1

[Pham Van Hung]

\(0< a< 1\Rightarrow\hept{\begin{cases}a>0\\a-1< 0\end{cases}\Rightarrow}a\left(a-1\right)< 0\Rightarrow a^2-a< 0\Rightarrow a^2< a\Rightarrow a< \sqrt{a}\)

Vậy nếu 0 < x < 1 thì \(\sqrt{a}>a\)