已知a.b.c为正实数,求(a*2b*2+b*2c*2+c*2a*2)/(a+b+c)大于等于abc
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![已知a.b.c为正实数,求(a*2b*2+b*2c*2+c*2a*2)/(a+b+c)大于等于abc](/uploads/image/z/568200-48-0.jpg?t=%E5%B7%B2%E7%9F%A5a.b.c%E4%B8%BA%E6%AD%A3%E5%AE%9E%E6%95%B0%2C%E6%B1%82%28a%2A2b%2A2%2Bb%2A2c%2A2%2Bc%2A2a%2A2%29%2F%28a%2Bb%2Bc%29%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8Eabc)
已知a.b.c为正实数,求(a*2b*2+b*2c*2+c*2a*2)/(a+b+c)大于等于abc
已知a.b.c为正实数,求(a*2b*2+b*2c*2+c*2a*2)/(a+b+c)大于等于abc
已知a.b.c为正实数,求(a*2b*2+b*2c*2+c*2a*2)/(a+b+c)大于等于abc
A^2B^2+B^2C^2=B^2(A^2+C^2)>=2*ACB^2
同理b^2c^2+c^2a^2>=2*abc^2
a^2b^2+c^2a^2>=2*bca^2
以上3式相加,两边同除2,证毕
(a*2b*2+b*2c*2+c*2a*2)/(a+b+c)-abc只要证明a*2b*2+b*2c*2+c*2a*2-(a+b+c)*abc>=0即可
大于