Moved - l Equation Prove NEED HELP!!

[kuso125789]

Assume a, b, c≥0 and a, b, c∈R satisfy abc≥1
Proof: a³+b³+c³≥ab+bc+ca

Thanks to every one!

 

[Deleted member 4993]

Assume a, b, c≥0 and a, b, c∈R satisfy abc≥1
Proof: a³+b³+c³≥ab+bc+ca

Thanks to every one!

a³ + b³ + c³ - 3abc = (a + b + c) * (a² + b² + c² - ab - bc - ca)

 

[kuso125789]

a³ + b³ + c³ - 3abc = (a + b + c) * (a² + b² + c² - ab - bc - ca)

I want to know how to proof a³+b³+c³≥ab+bc+ca, instead of multiplication formula.
Multiplication formula

 

[stapel]

I want to know how to proof a³+b³+c³≥ab+bc+ca, instead of multiplication formula.

The reply was not a misunderstanding of the question, but a hint as to a possible avenue of solution.