Question

若a＞1，则a+1/(a-1)的最小值是

麻烦一下过程~
A 2 B a
C3 D （2√a²-a）/（a-1）

Answer 1

原式=(a-1)+1/(a-1)+1
a>1,a-1>0
所以原式≥2√[(a-1)*1/(a-1)]+1=3
最小直3 C

Answer 2

(a-1 +2)/(a-1)
= 1 + 2/(a-1)
a无穷大的时候 2/(a-1) =0
最小为1

Answer 3

最小值是1.
a+1/(a-1)=(a-1+2)/(a-1)=1+2/(a-1).当a为无穷大时有最小值.=1+0=1

Answer 4

y=a+1/(a-1)在区间a>1上市单调递增函数，所以当a趋近于无穷大时a+1/(a-1)最小，值为1.

Answer 5

a+1/(a-1)=1+(a-1)+1/(a-1),因为a>1,所以a-1>0,所以（a-1）+1/(a-1)>2,即a+1/(a-1)>1