Question

Chứng minh:

 \(\left(3^{n+2}-2^{n+2}+3^n-2^n\right)⋮10\)

GIÚP MIK VỚI CÁC BẠN

Answer 1

\(3^{n+2}-2^{n+2}+3^n-2^n=3^n.\left(3^2+1\right)-2^n.\left(2^2+1\right)\)

\(=3^n.10-2^n.5=3^n.10-2^{n-1}.10=10.\left(3^n-2^{n-1}\right)⋮10\)

Answer 2

\(3^{n+2}-2^{n+2}+3^n-2^n\)

\(=3^n\times\left(3^2+1\right)-2^n\times\left(2^2+1\right)\)

\(=3^n\times10-2^n\times5\)

\(3^n\times10⋮10\)\(2^n\times5⋮10\)

=> \(3^{n+2}-2^{n+2}+3^n-2^n⋮10\)

Answer 3

3^n+2 - 2^n+2 +3^n - 2^n 

=> 3^n(3^2+1) - 2^n (2^2 + 1)

=> 10 . 3^n - 5 . 2^n 

=> 10 . 3^n - 10. 2^n-1

=>10 . (3^n - 2^n-1 ) chia hết cho 10

=> ĐPCM