Difficult Inequalities Proof

As much help as possible would be appreciated for this difficult problem I have been stressing over for the past few days!

Prove that [(x^3 + y^3 + z^3)/3]^2 is greater than or equal to [(x^2 + y^2 + z^2)/3]^3

really need a solid proof to this questions as quickly as possible!
Thanks

Sorry, someone please delete this.. I need sleep before tackling anything else :(

Quote:

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Originally Posted by will_fang

As much help as possible would be appreciated for this difficult problem I have been stressing over for the past few days!

Prove that [(x^3 + y^3 + z^3)/3]^2 is greater than or equal to [(x^2 + y^2 + z^2)/3]^3

really need a solid proof to this questions as quickly as possible!
Thanks

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x,y,z real numbers ??