若实数a.b满足:ab-4a-b+1=0(a>1),则(a+1)(b+2)的最小值是

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/16 16:20:34
若实数a.b满足:ab-4a-b+1=0(a>1),则(a+1)(b+2)的最小值是若实数a.b满足:ab-4a-b+1=0(a>1),则(a+1)(b+2)的最小值是若实数a.b满足:ab-4a-b

若实数a.b满足:ab-4a-b+1=0(a>1),则(a+1)(b+2)的最小值是
若实数a.b满足:ab-4a-b+1=0(a>1),则(a+1)(b+2)的最小值是

若实数a.b满足:ab-4a-b+1=0(a>1),则(a+1)(b+2)的最小值是
我最喜欢这种题目
a>1有a-1>0
ab-4a-b+1=0(a>1)
那么b=(4a-1)/(a-1)
那么f(a)=(a+1)(b+2)=(a+1)((4a-1)/(a-1)+2)
=(6a-3)(a+1)/(a-1)=6(a-1)+[6/(a-1)]+15≥12+15=27
取等条件是1/(a-1)=a-1
那么a-1=1,得a=2