How to show that a^3 + b^3 ≥ abc(a/c + b/c)

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How to show that a^3/b + b^3/c + c^3/a ≥ ab + bc + ac How to show that a^3/b + b^3/c + c^3/a ≥ ab + bc + ac
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How to show that (a^3 + b^3 + c^3)/3 ≥ abc How to show that (a^3 + b^3 + c^3)/3 ≥ abc
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