Inequality

[Iroki]

Hey guys, how is life going?? Is there anybody very good at math??
I have a problem with hard inequality.. very hard :)



Positive x, y, z (real) are given such that x^4 + y^4 + z^4 >= x^3 + y^3 + z^3

Prove that:

x^3/sqrt(y^4 + y^2*z^2 + z^4) + y^3/sqrt(z^4 + z^2*x^2 + x^4) + z^3/sqrt(x^4 + x^2*y^2 + y^4) >= sqrt(3)

Any ideas how to prove that?

[lollage22]

Do yo ustill need the answer? :)