Question

a∈R

$2^{a-1}$,$2^{-a+2}+1$, $2^{a+1}+1$ progresie aritmetica


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Answer 1

Răspuns:

$2*(2^{-a+2}+1)=2^{a-1}+2^{a+1}+1,~2^{3-a}+1=\frac{2^{a}}{2}+2*2^{a},~\frac{8}{2^{a}}+1 = \frac{2^{a}}{2}+2*2^{a},~|*2*2^{a},~5*(2^{a})^{2}-2*2^{a}-16=0,~fie~2^{a}=t>0,~\\5t^{2}-2t-16=0,~delta=324,~\sqrt{324}=18,~t=2,~deci~2^{a}=2^{1},~deci~a=1.$

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