a+b=1(a>0,b>0),求证:(a+1/a)(b+1/b)>=25/4已知a+b=1(a>0,b>0)求证:(a+1/a)(b+1/b)>=25/4
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![a+b=1(a>0,b>0),求证:(a+1/a)(b+1/b)>=25/4已知a+b=1(a>0,b>0)求证:(a+1/a)(b+1/b)>=25/4](/uploads/image/z/10022048-8-8.jpg?t=a%2Bb%3D1%EF%BC%88a%3E0%2Cb%3E0%EF%BC%89%2C%E6%B1%82%E8%AF%81%EF%BC%9A%EF%BC%88a%2B1%2Fa%EF%BC%89%EF%BC%88b%2B1%2Fb%EF%BC%89%3E%3D25%2F4%E5%B7%B2%E7%9F%A5a%2Bb%3D1%EF%BC%88a%3E0%2Cb%3E0%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9A%EF%BC%88a%2B1%2Fa%EF%BC%89%EF%BC%88b%2B1%2Fb%EF%BC%89%3E%3D25%2F4)
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a+b=1(a>0,b>0),求证:(a+1/a)(b+1/b)>=25/4已知a+b=1(a>0,b>0)求证:(a+1/a)(b+1/b)>=25/4
a+b=1(a>0,b>0),求证:(a+1/a)(b+1/b)>=25/4
已知a+b=1(a>0,b>0)
求证:(a+1/a)(b+1/b)>=25/4
a+b=1(a>0,b>0),求证:(a+1/a)(b+1/b)>=25/4已知a+b=1(a>0,b>0)求证:(a+1/a)(b+1/b)>=25/4
ab+a/b+1/ab+b/a
=(a平方b平方+a平方+1+b平方)/ab
=[a平方b平方+(1-2ab)+1]/ab
=[(ab-1)平方+1]/ab
a+b=1
ab
a=b=0.5相等时取得最小值
原式成立
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