Question

当x大于1时,不等式x+(x-1)分之1大于等于a恒成立,则a的取值?

Answer 1

要使x+1/(x-1)≥a对x>1恒成立,只要x+1/(x-1)的最小值都大于等于a即可.

而当x>1时,x-1>0,有

x+1/(x-1)=(x-1)+1/(x-1)+1

≥2√(x-1)*1/(x-1)+1

=3

当且仅当x-1=1/(x-1)即x=2（x=0舍去）时,取得等号.

所以该式最小值为3.于是有：a≤3.