Giải Bài tập 7 trang 13 Toán 11 tập 2 Chân trời

a) $16^{\alpha} + 16^{-\alpha} = 16^{\alpha} + \frac{1}{16^{\alpha}}=(4^{2})^{\alpha} +  \frac{1}{(4^{2})^{\alpha}} =(4^{\alpha})^{2}+\frac{1}{(4^{\alpha})^{2}}$

$=  \left ( \frac{1}{5} \right )^{2}+\frac{1}{\left ( \frac{1}{5} \right )^{2}} = \frac{1}{25}+\frac{1}{\frac{1}{25}}=\frac{1}{25}+25=\frac{626}{25}$

b) $(2^{\alpha} + 2^{-\alpha})^{2}  = (2^{\alpha})^{2}+2.2^{\alpha}.2^{-\alpha} + (2^{-\alpha})^{2} = (2^{2})^{\alpha} + 2^{1+\alpha-\alpha}+(2^{2})^{-\alpha}$

$= 4^{\alpha}+2+4^{-\alpha} = 4^{\alpha}+2+\frac{1}{4^{\alpha}} = \frac{1}{5}+2+\frac{1}{\frac{1}{5}}=\frac{36}{5}$