问个算术几何均值不等式的问题http://hiphotos.baidu.com/%C1%F8%F6%AD%D6%AE%C1%D6/pic/item/f0511f133be1bf36cb80c484.jpg设x=ab,y=bc,z=ca不等式等价于x^3+y^3+z^3>=xy^2+yz^2+zx^2AM-GM x^3+y^3+y^3>=3xy^2,y^3+z^3+z^3>=3yz^2,z^3+x^3+x^3>=3
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/27 16:09:50
![问个算术几何均值不等式的问题http://hiphotos.baidu.com/%C1%F8%F6%AD%D6%AE%C1%D6/pic/item/f0511f133be1bf36cb80c484.jpg设x=ab,y=bc,z=ca不等式等价于x^3+y^3+z^3>=xy^2+yz^2+zx^2AM-GM x^3+y^3+y^3>=3xy^2,y^3+z^3+z^3>=3yz^2,z^3+x^3+x^3>=3](/uploads/image/z/5130845-53-5.jpg?t=%E9%97%AE%E4%B8%AA%E7%AE%97%E6%9C%AF%E5%87%A0%E4%BD%95%E5%9D%87%E5%80%BC%E4%B8%8D%E7%AD%89%E5%BC%8F%E7%9A%84%E9%97%AE%E9%A2%98http%3A%2F%2Fhiphotos.baidu.com%2F%25C1%25F8%25F6%25AD%25D6%25AE%25C1%25D6%2Fpic%2Fitem%2Ff0511f133be1bf36cb80c484.jpg%E8%AE%BEx%3Dab%2Cy%3Dbc%2Cz%3Dca%E4%B8%8D%E7%AD%89%E5%BC%8F%E7%AD%89%E4%BB%B7%E4%BA%8Ex%5E3%2By%5E3%2Bz%5E3%3E%3Dxy%5E2%2Byz%5E2%2Bzx%5E2AM-GM+x%5E3%2By%5E3%2By%5E3%3E%3D3xy%5E2%2Cy%5E3%2Bz%5E3%2Bz%5E3%3E%3D3yz%5E2%2Cz%5E3%2Bx%5E3%2Bx%5E3%3E%3D3)
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