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## Homework Statement

If a, b and c are distinct positive numbers, show that

[itex]

2 (a^3 + b^3 + c^3) > a^2b + a^2c + b^2c + b^2a + c^2a + c^2b

[/itex]

## Homework Equations

## The Attempt at a Solution

I have tried to expand from [tex](a+b+c)^3 > 0[/tex], also tried [tex](a+b)^3 + (b+c)^3 + (c+a)^3 > 0[/tex], and then [tex]\frac{a+b+c}{3} > \sqrt[3]{abc}[/tex]. But with no avail. I guess I'm heading in the wrong direction?

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