Giải bài 20 trang 82 SGK giải tích nâng cao 12

$a)\dfrac{1}{2}\left( {{a}^{\alpha }}+{{a}^{-\alpha }} \right)=1\,\, \\ \Leftrightarrow {{a}^{\alpha }}+{{a}^{-\alpha }}=2 \\ \Leftrightarrow \dfrac{{{a}^{2\alpha }}-2{{a}^{\alpha }}+1}{{{a}^{\alpha }}}=0 \\ \Leftrightarrow \dfrac{\left( {{a}^{\alpha }}-1 \right)}{{{a}^{\alpha }}}=0 \\ \Leftrightarrow {{a}^{\alpha }}-1=0$

Nếu $a\ne 1\Leftrightarrow \alpha =0$.

Nếu $a=1\Leftrightarrow \alpha$ tùy ý.

$\begin{align} & b)\,{{3}^{\left| \alpha \right|}}<27 \\ & \Leftrightarrow {{3}^{\left| \alpha \right|}}<{{3}^{3}} \\ & \Leftrightarrow \left| \alpha \right|<3 \\ & \Leftrightarrow -3<\alpha <3 \\ \end{align}$