已知,a>0,b>0,a+b=1,求证（1+1/a）（1+1/b)大于等于9

(1+1/a)(1+1/b)
=(a+1)/a*(b+1)/b
=(ab+a+b+1)/ab
=(ab+2)/ab
=1+2/ab
(a-b)^2>=0
(a+b)^2>=4ab
ab=8
(1+1/a)(1+1/b)>=9.
a=b=1/2时,取等号.