Question

Chứng minh rằng: Nếu 0 < a <1 thì

Answer 1

0<a<1

<=>he

a>0(1)

a<1(2)

(2)<=>√a<√1=1

<=>√a.√a<1.√a

<=>a<√a=>dpcm

Answer 2

Ta có :

\(\sqrt{a}>a\)

\(\Leftrightarrow\left\{{}\begin{matrix}a\ge0\\a>a^2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}a\ge0\\\left\{{}\begin{matrix}a\ne0\\a< 1\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow0< a< 1\)