UC知道两道解答题10.13
来源：百度知道 编辑：UC知道 时间：2024/05/11 05:15:31
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(1)已知:1/C5(m)-1/C6(m)=7/(10*C7(m),
求C8(m)
解:
C5(m)=5!/[(5-m)!m! C6(m)=6!/[(6-m)!m!
C7(m)=7!/[(7-m)!m!
代入到已知条件,
(5-m)!m!/5!-(6-m)!m!/6!=7*(7-m)!m!/(10*7!),
1-(6-m)/6=7*(7-m)(6-m)/(10*7*6)
化简后得到,
m^2-23m+42=0,解得,m1=21,(大于8,舍去),m2=2.
把m=2,代入C8(m)=8*7/2=28.
C8(m)=28.
(2)已知,Cn[(m-1)]/2=Cn(m)/3=Cn[(m+1)]/4,
求m与n.
解:Cn[(m-1)]=n!/[(n-m+1)!(m-1)!],
Cn(m)=n!/(n-m)!m!
Cn!/[(n-m-1)!(m+1)!]有,
n!/2[(n-m+1)!(m-1)!]=Cn(m)=n!/3(n-m)!m!,
Cn(m)=n!/3(n-m)!m!=Cn!/4[(n-m-1)!(m+1)!],
化简后得,
1/2(n-m+1)=1/3,
1/3(n-m)=1/4(m+1),
得,2n-2m-1=0,3n-7m-4=0.解得
n=9/8,m=-5/8.