b+3a-ab=0,求a+2b的最小值 a>0,b>0

b+3a-ab=0,求a+2b的最小值 a>0,b>0

由已知可知a不等於1,由b+3a-ab=0可得b=3a/(a-1),囙此有
a+2b=a+6a/(a-1)=(a^2+5a)/(a-1),令a-1=t,t不等於0,則有a=t+1,代入有
a+2b=[(t+1)^2+5(t+1)]/t=t+7+6/t>=7+2*sqrt6