Question

Cho số m dương.Chứng minh:

a) Nếu m > 1 thì \(\sqrt{m}\)>1.

b) Nếu m < 1 thì \(\sqrt{m}\)<1.

Answer 1

a, Nếu m > 1 thì $\sqrt[2]{2m}$ > 1
ta có
$m>1\iff m-1>0\iff \backslash (\backslash left(\backslash sqrt\{m\}-1\backslash right)\backslash left(\backslash sqrt\{m\}+1\backslash right)>0\backslash )\iff \backslash (\backslash sqrt\{m\}-1\backslash )>0$ => đpcm
(do m dương nên \(\sqrt{m}-1\)$>0$)

Answer 2

ta có:

\(m>1\Leftrightarrow m-1>0\Leftrightarrow\left(\sqrt{m}-1\right)\left(\sqrt{m}+1\right)>0\)

\(\Leftrightarrow\sqrt{m}-1>0\Rightarrowđpcm\) ( do m dương nên \(\sqrt{m}+1>0\)  )