Question

Chứng minh rằng:

a) A = ( x+3 )( x+7 )( x+11 ) : 3 với x ϵ N

b) B= x( x+1 )( 2x+1 ) : 3 với x ϵ N

Answer 1

a: Trường hợp 1: x=3k

\(\Leftrightarrow A=\left(3k+3\right)\left(3k+7\right)\left(3k+11\right)⋮3\)

Trường hợp 2: x=3k+1

\(\Leftrightarrow A=\left(3k+4\right)\left(3k+8\right)\left(3k+12\right)⋮3\)

Trường hợp 3: x=3k+2

\(\Leftrightarrow A=\left(3k+5\right)\left(3k+9\right)\left(3k+13\right)⋮3\)