(a-b)^3=a^3-3a^2b+3ab^2-b^3(x+y)(x^3+y^3)大于等于0
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![(a-b)^3=a^3-3a^2b+3ab^2-b^3(x+y)(x^3+y^3)大于等于0](/uploads/image/z/1999214-62-4.jpg?t=%28a-b%29%5E3%3Da%5E3-3a%5E2b%2B3ab%5E2-b%5E3%28x%2By%29%28x%5E3%2By%5E3%29%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E0)
(a-b)^3=a^3-3a^2b+3ab^2-b^3(x+y)(x^3+y^3)大于等于0
(a-b)^3=a^3-3a^2b+3ab^2-b^3
(x+y)(x^3+y^3)大于等于0
(a-b)^3=a^3-3a^2b+3ab^2-b^3(x+y)(x^3+y^3)大于等于0
(x+y)(x^3+y^3)
=(x+y)^2(x^2-xy+y^2)
=(x+y)^2[(x-y/2)^2+3y^2/4]
因为(x-y/2)^2>=0,3y^2/4>=0
所以(x-y/2)^2+3y^2/4>=0
又(x+y)^2>=0
所以(x+y)(x^3+y^3)>=0