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

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

若实数a,b满足ab-4a-b+1=0(a>1),则(a+1)(b+2)的最小值为?
ab+b+2a+2
ab-4a-b+1==0
所以
ab+ab-4a+1+2a+2==2ab-2a+3
b==(4a-1)/(a-1) (a>1)
===4+3/(a-1)
原式===6a+6a/(a-1)+3
===6a+6/(a-1)+9
==6(a-1)+6/(a-1)+15
在a==2时最小值为 12+15===27