若实数a,b满足ab一4a一b十1=0(a>1),求(a+1)(b+2)的最小值
问题描述:
若实数a,b满足ab一4a一b十1=0(a>1),求(a+1)(b+2)的最小值
答
∵a>1,∴a-1>0.令(a+1)(b+2)=k,则:ab+2a+b+2=k,又ab-4a-b+1=0,∴(ab+2a+b+2)-(ab-4a-b+1)=k,∴6a+2b+1=k,∴b=(k-1-6a)/2.将b=(k-1-6a)/2代入到ab-4a-b+1=0中,得:a...