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Question Number 21566 by mondodotto@gmail.com last updated on 27/Sep/17

Commented by mrW1 last updated on 27/Sep/17

$$\frac{1}{2^2}+\frac{3}{2^2}=\frac{1}{4}+\frac{3}{4}=1$$$$\Rightarrow \mathrm{a}=2$$

Commented by FilupS last updated on 27/Sep/17

$$\mathrm{Similarly},\mathrm{thinking}\mathrm{logically}:$$$$\mathrm{for}\frac{1}{a^2}+\frac{3}{2^a}=1$$$$\Rightarrow LHS\mathrm{must}\mathrm{equal}\frac{x}{x}=\frac{1}{1}$$$$\therefore \mathrm{if}{a}^2=2^a=u,\mathrm{then}:\frac{1+3}{u}=1$$$$\therefore u=4$$$$$$$$\mathrm{then},\mathrm{you}\mathrm{can}\mathrm{test}\mathrm{you}\mathrm{solution}$$$$$$$$\therefore a^2=4,a=\pm 2$$$$$$$$2^a=4,\therefore a=2a\ne -2$$$$$$$$\therefore a=2$$

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