Question

2 la puterea 50+2 la puterea 52 comparat cu 5 la puterea 21
VA ROG E URGENTTT
DAU COROANA​

Answer 1

$\displaystyle{ 2^{50} + 2^{52} = 2^{50} \cdot (1 + 2^{2}) = 2^{50} + (1 + 4) = 5 \cdot 2^{50} }$

$\displaystyle{ 5^{21} = 5^{20} \cdot 5 }$

Impartim ambele numere prin 5.

Trebuie comparat:

$\displaystyle{ 5^{20} \ cu \ 2^{50} }$

$\displaystyle{ 5^{20} = (5^{2})^{10} = 25^{10} }$

$\displaystyle{ 2^{50} = (2^{5})^{10} = 32^{10} }$

$\displaystyle{ 25^{10} < 32^{10} \rightarrow 5^{21} < 2^{50} + 2^{52} }$

Matei