Question

Mình đang cần gấp:

\((n+45)(4n^2-1)\) chia hết cho 3

Hứa tick

 

 

Answer 1

Xét \(n=3k\) thì :

\(3k+45⋮3\Rightarrow\left(n+45\right)\left(4n^2-1\right)⋮3\)

Xét \(n=3k+1\) thì :

\(4.\left(3k+1\right)^2-1=4.\left(9k^2+6k+1\right)-1=36k^2+24k+3⋮3\)

\(\Rightarrow\left(n+45\right)\left(4n^2-1\right)⋮3\)

Xét \(n=3k-1\) thì :

\(4.\left(3k+1\right)^2-1=4.\left(9k^2-6k+1\right)-1=36k^2-24k+3⋮3\)

\(\Rightarrow\left(n+45\right)\left(4n^2-1\right)⋮3\)

Vậy \(\left(n+45\right)\left(4n^2-1\right)⋮3\forall n\inℤ\)