Question

cminh:

a)((2n+3)^2-9):4 voi moi n thuoc z

b)((3n+4)^2-16:3 voi moi n thuoc z

 

Answer 1

\(\left(2n+3\right)^2-9=\left(2n+3\right)^2-3^2=\left(2n+3-3\right)\left(2n+3+3\right)=2n\left(2n+6\right)=4n\left(n+3\right)⋮4\)

\(\left(3n+4\right)^2-16=\left(3n+4\right)^2-4^2=\left(3n+4-4\right)\left(3n+4+4\right)=3n\left(3n+8\right)⋮3\)

Answer 2

a) ta có: (2n+3)² - 9

= 4n² +12n + 9 - 9

= 4n.(n+3) chia hết cho 4

=> ...

b) ta có: (3n+4)² - 16

= 9n² + 24n + 16 - 16

= 3n.(3n + 8)  chia hết cho 3

=> ...