Question

Arătați ca:

2^6n|(8^2n+1+4^3n+1-11*64^n)


^ înseamnă "la puterea"
| înseamnă"divide"
* înseamnă "ori"

Answer 1

   
[tex] 2^{6n}~|~(8^{2n+1}+4^{3n+1}-11\times 64^n)\\ \\ \text{Rezolvare: } \\ \\ 8^{2n+1}+4^{3n+1}-11\times64^n=\\ = 8^{2n}\times8+4^{3n}\times4-11\times 64^n=\\ =8\times(2^3)^{2n}+4\times(2^2)^{3n}-11\times(2^6)^n=\\ =8\times2^{3\times2n}+4\times2^{2\times3n}-11\times2^{6\times n}=\\ =8\times2^{6n}+4\times2^{6n}-11\times 2^{6n}=\\ 2^{6n}\times(8+4-11) 2^{6n}\times1 = \boxed{2^{6n}} \\ \\ \boxed{2^{6n}~|~2^{6n}}[/tex]