AMATHS的bio題目一條

用戶206103

2007-10-01 2:16 am

C:上面20 C:上面20
下面2R+1= 下面2R+3
FIND THE VALUE OF R

更新1:

各位大大可唔可以解得詳小小-.- 小弟很笨咧=3=

回答 (1)

我是貓

2007-10-01 2:52 am

✔ 最佳答案

C:上面20 下面2R+1 = C:上面20下面2R+3 可以寫成
20C2R+1 = 20C2R+3

20C2R+1 = 20! / [(2R+1)! (20-2R-1)!]
20C2R+3 = 20! / [(2R+3)! (20-2R-3)!]

兩者相等
=> (2R + 1)! (20 – 2R –1)! = (2R + 3)! (20 – 2R –3)!
=> (2R + 1)! (20 – 2R – 1) (20 – 2R –2) (20 – 2R –3)! = (2R + 3) (2R + 2) (2R + 1)! (20 – 2R –3)!
=> (20 – 2R – 1) (20 – 2R –2) = (2R + 3) (2R + 2)
=> (19 – 2R) (18 – 2R) = (2R + 3) (2R + 2)
=> (19 – 2R) (9 – R) = (2R + 3) (R + 1)
=> 171 – 37R + 2R2 = 2R2 + 5R + 3
=> 168 = 42R
=> R = 4

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