若x,y都是正数,且xy=x+y+3,则xy的取值范围是

Question

若x,y都是正数,且xy=x+y+3,则xy的取值范围是                                     
 

Answer 1

x>0,y>0
x+y>=2√(xy)
x+y=xy-3
所以xy-3>=2√(xy)
xy-2√(xy)-3>=0
[√(xy)-3][√(xy)+1]>=0
√(xy)>=0
所以√(xy)>=3
xy>=9