Question

若正數a,b滿足ab=a+b+3,則ab的取值范圍是__________.

Answer 1

解析:由ab=a+b+3,得b=,

兩邊同乘以a,得ab=a+=a+4+=a-1++5.?

又由ab=a+b+3,得b(a-1)=a+3＞0.?

所以a-1＞0.?

所以a-1++5≥+5=9,

當且僅當a=3時取等號.所以ab的取值范圍是［9,?+∞).??

答案:［9,+∞).