问题
填空题
若xn+…+ax3+bx2+cx+4n=(x+4)n(n∈N+,n≥3)且a:b=3:2,则n=______.
答案
依题意,a=
4n-3,b=C 3n
4n-2,C 2n
∵a:b=3:2,
∴
=
4n-3C 3n
4n-2C 2n
=n(n-1)(n-2) 6
×4n(n-1) 2
=n-2 12
,3 2
解得n=20.
故答案为:20.
若xn+…+ax3+bx2+cx+4n=(x+4)n(n∈N+,n≥3)且a:b=3:2,则n=______.
依题意,a=
4n-3,b=C 3n
4n-2,C 2n
∵a:b=3:2,
∴
=
4n-3C 3n
4n-2C 2n
=n(n-1)(n-2) 6
×4n(n-1) 2
=n-2 12
,3 2
解得n=20.
故答案为:20.