by henderson, Jun 10, 2016, 7:19 PM 
Show that for non-negative real numbers 
the following inequality holds![\[2(a^6+b^6+c^6)+16(a^3b^3+b^3c^3+c^3a^3)\geq 9a^4(b^2+c^2)+9b^4(c^2+a^2)+9c^4(a^2+b^2).\]](http://latex.artofproblemsolving.com/a/b/9/ab9ae0aa029cb8043d73f7bc48a67c5e68984b97.png)
![\[LHS-RHS=\sum_{cyc}{\left((a-b)^2(a^4+2a^3b+2ab^3+b^4-6a^2b^2)\right)},\]](http://latex.artofproblemsolving.com/3/2/e/32e1127796c393f19045f3829280ae2c4ecf2d03.png)
which is clearly non-negative."Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater." - Albert Einstein
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