Question

Chứng minh rằng:

a) 3ⁿ⁺³ + 3ⁿ⁺¹ + 2ⁿ⁺³ + 2ⁿ⁺² chia hết cho 6 (n \(\in\) N*)

b) 12⁸.9¹²=18¹⁶

Answer 1

=3^n.9+3^n.3+2^n.8+2^n.4

=3^n[9+3]+2^n[8+4]

=3^n.12+2^n.12chia hết cho 6[vị 12 chia hết cho 6]

b,=12^8.9^12

=2^16.3^8.3^24

=2+16.3^32

18^16=2^16.3^32

suy ra bằng nhau

Answer 2

\(12^8.9^{12}=4^8.3^8.9^{12}=2^{16}.9^4.9^{12}==2^{16}.9^{16}=\left(2.9\right)^{16}=18^{16}\)