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Demonstrati ca numarul [tex] 4^{2} ^{n}+ 2^{2} ^{n} ^{+1} +1[/tex] , n∈N,este pătrat perfect.

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Răspuns :

(4^n +1)^2=
4^2n+2*4^n*1+1=
4^2n+2*2^2n+1=
4^2n+2^(2n+1)+1
⇒este patrat perfect




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