a+b=1,求(a+1/a)(b+1/b)大于等于25/4a大于0,b大于0,a+b=1,求证(a+1/a)(b+1/b)大于等于25/4
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a+b=1,求(a+1/a)(b+1/b)大于等于25/4a大于0,b大于0,a+b=1,求证(a+1/a)(b+1/b)大于等于25/4
a+b=1,求(a+1/a)(b+1/b)大于等于25/4
a大于0,b大于0,a+b=1,求证
(a+1/a)(b+1/b)大于等于25/4
a+b=1,求(a+1/a)(b+1/b)大于等于25/4a大于0,b大于0,a+b=1,求证(a+1/a)(b+1/b)大于等于25/4
1=a+b>=2根号(ab),根号(ab)
第一题配凑平均不等式的方法
a+1/a=a+1/(4a)+1/(4a)+1/(4a)+1/(4a)≥5/(4^4a^3)^(1/5),
同理
b+1/b≥5/(4^4b^3)^(1/5),
所以
(a+1/a)(b+1/b)≥25/(4^8(ab)^3)^(1/5)。
另外
ab≤((a+b)/2)^2=1/4,
所以
(a+1/a)(b+1/b)≥25/(4^8/4^3)^(1/5)=25/4,
pig