Question

arătați ca x=4^n×3^2n+1+2^2n+3×9^n se divide cu 11​

Answer 1

Salut.

$\displaystyle{x=4^{n}\times3^{2n+1}+2^{2n+3}\times9^{n} }$

• Descompunem expresia în factori.

$\displaystyle{x=2^{2n} \times 3^{2n+1}+2^{2n+3}\times3^{2n} }$

$\displaystyle{x=(3 +2^{3})\times2^{2n}\times3^{2n} }$

• Calculăm paranteza.

$\displaystyle{x=(3+8)\times2^{2n}\times3^{2n} }$

$\displaystyle{x=11\times2^{2n}\times3^{2n} }$

$\displaystyle{x=11\times6^{2n} }$

$\displaystyle{x=11\times36^{n} }$

=> $\displaystyle{x}$ se divide cu 11

=> adevărat

- Lumberjack25