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