设a>0,b>0,a+b=1.求证:1/a+1/b+1/ab>=8

设a>0,b>0,a+b=1.求证:1/a+1/b+1/ab>=8
设a>0,b>0,a+b=1.求证:1/a+1/b+1/ab>=8

设a>0,b>0,a+b=1.求证:1/a+1/b+1/ab>=8
设a>0,b>0,且a+b=1,求证：1/a+1/b+1/(a*b)>=8
(a+b)^2>=4ab
01/a+1/b+1/ab [通分]
=(a+b+1)/ab =2/ab >=8
所以1/a+1/b+1/ab>=8
a=b=1/2时 取等号

1/a+1/b+1/ab＝(a+b+1)/ab=2/(ab)>=2/(1/2 *1/2)=8