Question

Am adresat o intrebare la care nu am primit niciun raspuns. Oare nimeni nu poate rezolva exercitiul???
Revin cu enuntul: Aratati ca numarul 8^(n+1) + 9*8^n + 10*2^3n este cub perfect.
Astept elevi isteti si multumesc!

Answer 1

8^(n+1) + 9*8^n + 10*2^3n
8^(n+1) + 9*8^n + 10*8^n
8^n*(8+9+10)
8^n*27
8^n*3^3=2^3n*3^3=(2^n*3)^3 => cub perfect

Answer 2

$8^{n+1}+9\cdot8^n+10\cdot2^3^n\rightarrow cub~perfect \\ 8^n\cdot8+9\cdot8^n+10\cdot(2^3)^n= \\ =8^n\cdot8+9\cdot8^n+10\cdot8^n= \\ =8^n(8+9+10)= \\ =8^n\cdot27=\\=2^3^n\cdot3^3=(2^n\cdot3)^3=cub~perfect\\Bafta! ~ ;)$