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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

(1/2^2 )+(3/2^2 )=(1/4)+(3/4)=1  ⇒a=2

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

Commented by FilupS last updated on 27/Sep/17

Similarly, thinking logically:  for   (1/a^2 )+(3/2^a )=1  ⇒LHS must equal (x/x)=(1/1)  ∴if a^2 =2^a =u, then: ((1+3)/u)=1  ∴u=4     then, you can test you solution     ∴a^2 =4,  a=±2     2^a =4,   ∴a=2      a≠−2     ∴a=2

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

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