已知x,y为正数,且x+y=1.求证：（1+1/x)(1+1/y)>9或等于9

(1+1/x)(1+1/y)
=(1+(x+y)/x)(1+(x+y)/y)
=(2+y/x)(2+x/y)
=4+2(x/y+y/x)+1
=5+2(x/y+y/x)
>=5+2*2√(x/y*y/x)
=5+2*2
=9