Question

Va rog rezolvatile dau 20 pucte
Dau si coroană va roggggggggggg
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Answer 1

$\displaystyle{ A = 2^{2012} + 2^{2011} + 2^{2010} + 2^{2009} }$

$\displaystyle{ A = 2^{2009} \cdot (2^{3} + 2^{2} + 2 + 1) }$

$\displaystyle{ A = 2^{2009} \cdot (8 + 4 + 2 + 1) }$

$\displaystyle{ A = 2^{2009} \cdot 15 \ \vdots \ 15 }$

q.e.d.

$\displaystyle{ B = 3^{999} + 3^{1001} + 3^{1003} }$

$\displaystyle{ B = 3^{999} \cdot (1 + 3^{2} + 3^{4}) }$

$\displaystyle{ B = 3^{999} \cdot (1 + 9 + 81) }$

$\displaystyle{ B = 3^{999} \cdot 91 \ \vdots \ 91 }$

q.e.d.

PS: Rezolvati-le se scrie cu cratima!