Question

已知互不相等的实数a、b、c满足a+1/b=b+1/c=c+1/a=t,则t=?

Answer 1

因为已知互不相等的实数a、b、c满足a+1/b=b+1/c=c+1/a=t
令b=1,
则a+1/b=b+1/c
a+1=1+1/c
a=1/c
b+1/c=c+1/a
1+1/c=c+1/(1/c)=2c
1+1/c=2c
2c^2-c-1=0
(2c+1)(c-1)=0
得c=1或c=-1/2
因为a、b、c互不相等，所以c=-1/2
a=1/c=-2
所以t=a+1/b=-2+1=-1

Answer 2

(a+1)/b=(b+1)/c=(c+1)/a=t
a+1=bt
b+1=ct
c+1=at
以上3式相加得
a+b+c+3=(a+b+c)t
t=(a+b+c+3)/(a+b+c)

Answer 3

正确答案正负一