THQ266

 Problem. (Tạ Hồng Quảng) 

For $a,b,c>0;a+b+c=1.$ Prove:

$$ {\dfrac {{a}^{3}}{b}}+{\dfrac {{b}^{3}}{c}}+{\dfrac {{c}^{3}}{a}}- { \dfrac { \left( q+1 \right) \left( 3-8\,q \right) }{4q}}\geqslant {\dfrac { \left( 1-3\,q \right) \left( 1-4\,q \right) ^{2} \left( 882\,{q}^{2} -552\,q+293 \right) }{108\,q \left( 1-2\,q \right) \left( 11-12\,q \right) }} $$

Solution. (tthnew)

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