<s>[INST] For positive real numbers $a,b,c$ prove that $ a^4 + b^4 + c^4 \ge abc(a+b+c)$ For positive reals $a,b,c$ prove that $$ a^4+b^4+c^4 \ge abc(a+b+c). $$
I tried to pls around trying to reorganize to get AM-GM but i couldn't 
Thanks for the help in advance.
 [/INST] By AM_GM we get
\begin{align*}
\frac{2a^4+b^4+c^4}{4} & \geq a^2bc\\
\frac{2b^4+a^4+c^4}{4} & \geq b^2ac\\
\frac{2c^4+b^4+a^4}{4} & \geq c^2ab
\end{align*}
Now add these to get your inequality.
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