Question

CMR: (n-1)(3-2n)-n(n+5) chia hết cho 3 với mọi n

Answer 1

A=3n-2n^2-3+2n-n^2-5n

=-3 chia hết cho 3

Answer 2

 \(\left(n-1\right)\left(3-2n\right)-n\left(n+5\right)\)

\(=3n-2n^2-3+2n-n^2-5n\)

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

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

\(Vì\) \(-3\) \(⋮\) \(3\) nên \(-3\left(n^2+1\right)\) \(⋮\) \(3\)