Question

aratati ca nr n= 8• 6n + 10 • 6n+1 -6n+2 este dizivibil cu 8

va rog e pe nota asta rapid​

Answer 1

Răspuns: Ai demonstrația mai jos

Explicație pas cu pas:

$\bf n= 8\cdot 6^n + 10\cdot6^{n+1} -6^{n+2}$

$\bf n= 6^n \cdot \bigg(8\cdot 6^{n-n} + 10\cdot6^{n+1-n} -6^{n+2-n}\bigg)$

$\bf n= 6^n \cdot \Big(8\cdot 6^{0} + 10\cdot6^{1} -6^{2}\Big)$

$\bf n= 6^n \cdot \Big(8\cdot 1 + 10\cdot6 -36\Big)$

$\bf n= 6^n \cdot \Big(8 + 60 -36\Big)$

$\bf n= 6^n \cdot 32$

$\red{\boxed{~\bf n= 6^n \cdot 4\cdot 8\implies n~~\vdots~~8~}}$

$==pav38==$  

Answer 2

$\it 8\cdot6^n+10\cdot6^{n+1}-6^{n+2}=6^n(8+60-36)=6^n\cdot32=6^n\cdot4\cdot8\in M_8$