一道很易做錯的數學題

2011-02-28 3:37 am
已知 a/b = b/c = c/d = d/a ,

求(a+b+c+d) / (a+b+c-d) 的值。



回答 (7)

2011-02-28 5:20 am
✔ 最佳答案
sol
设a/b=b/c=c/d=d/a=k
a=bk
b=ck
c=dk
d=ak
相加
(a+b+c+d)=k(a+b+c+d)
(a+b+c+d)(k-1)=0

若a+b+c+d=0
则(a+b+c+d)/(a+b+c-d)=0
若k-1=0,k=1
则由a=bk
b=ck
c=dk
d=ak
得a=b=c=d
则(a+b+c+d)/(a+b+c-d)
=(a+a+a+a)/(a+a+a-a)
=4a/2a
=2

2011-02-27 21:24:29 補充:
◎ *TONY CHEUNG * ◎™ ( 碩士級 2 級 ):
you may right if a=0,but a/b is equil to inf. ...

2011-03-02 06:57:42 補充:
*例行提醒

請勿在得到答案後移除問題

2011-03-06 22:40:06 補充:
is m1 or m2?

2011-03-06 23:03:06 補充:
so you del by urself or...

2011-03-06 23:57:04 補充:
give me id card!
2011-03-06 8:51 pm
這是幾level的數?
2011-03-06 6:29 pm
Hok Yan :

我好喜歡你的解法 , 可惜你的最後答案0.75錯了 , 不能選你做最佳。

2011-03-06 22:46:09 補充:
很難界定什麼level....

2011-03-06 23:05:31 補充:
What do you mean?
2011-02-28 5:20 am
a/b × b/c × c/d × d/a = 1a^4/b^4 = 1b^4/c^4 = 1…如此類推,a^4= b^4= c^4= d^4= ±1a=c= -1 b=d=1 (a+b+c+d) / (a+b+c-d) =0ora=c= 1 b=d=-1 (a+b+c+d) / (a+b+c-d) =0or a=b=c=d= 1 (a+b+c+d) / (a+b+c-d) =0.75ora=b=c=d= -1 (a+b+c+d) /(a+b+c-d) =0.75

2011-02-28 09:13:12 補充:
a=b=c=d= 1 (a+b+c+d) / (a+b+c-d) =2

or

a=b=c=d= -1 (a+b+c+d) /(a+b+c-d) =2

2011-02-28 09:16:33 補充:
不是a^4= b^4= c^4= d^4= ±1

是a^2= b^2= c^2= d^2= 1
a=±1 b=±1 c=±1 d= ±1
2011-02-28 4:39 am
b^2=d^2=ac

a/b=c/d
bc=ad
__________________
a=b=c=d
(a+b+c+d) / (a+b+c-d)
4a/2a
=2
______________________
2011-02-28 4:00 am
2 or 0..............................
2011-02-28 4:00 am
a=b=c=d??
2????

2011-02-27 20:01:25 補充:
也是 有0這個東西...


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