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:作业帮 时间:2024/11/15 02:10:03

ab-4a-b+1=0,(a>1),则(a+1)(b+2)的最小值是?
ab-4a-b+1=0,(a>1),则(a+1)(b+2)的最小值是?

ab-4a-b+1=0,(a>1),则(a+1)(b+2)的最小值是?
ab-4a-b+1=0 →b=(4a-1)/(a-1)=4+3/(a-1) (a>1)
(a+1)(b+2)
=ab+b+2a+2
=a[4+3/(a-1) ]+4+3/(a-1) +2a+2
=6a+6a/(a-1)+3
=6a+6/(a-1)+9
=6(a-1)+6/(a-1)+15
=6[(a-1)+1/(a-1)]
当 a-1=1/(a-1)时取最大值
这时 a=2
最大值为:6×2+15=27