a) \({1 \over 2}\left( {{a^\alpha } + {a^{ - \alpha }}} \right) = 1 \Leftrightarrow {a^\alpha } + {a^{ - \alpha }} - 2 = 0 \Leftrightarrow {\left( {{a^{{\alpha \over 2}}} - {a^{ - {\alpha \over 2}}}} \right)^2} = 0 \Leftrightarrow {a^{{\alpha \over 2}}} = {a^{ - {\alpha \over 2}}}\)(*)
- Nếu \(a \ne \,1\) thì (*) \( \Leftrightarrow {\alpha \over 2} = - {\alpha \over 2} \Leftrightarrow \alpha = 0\)
- Nếu \(a = 1\) thì (*) \( \Leftrightarrow \alpha \) là số thực tùy ý.
b) \({3^{\left| \alpha \right|}} < 27 \Leftrightarrow {3^{\left| \alpha \right|}} < {3^3} \Leftrightarrow \left| \alpha \right| < 3 \Leftrightarrow - 3 < \alpha < 3.\)
