Question Number 154320 by mathdanisur last updated on 17/Sep/21
$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{ab}+\mathrm{bc}+\mathrm{ca}=\mathrm{2}\:\:\mathrm{then}: \\ $$ $$\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{a}\left(\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \right)}{\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{2}} \mathrm{c}\:+\:\mathrm{bc}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{3}} }\:\geqslant\:\mathrm{1} \\ $$
Answered by ghimisi last updated on 17/Sep/21
Commented bymathdanisur last updated on 17/Sep/21
$$\mathrm{Very}\:\mathrm{nice}\:\boldsymbol{\mathrm{S}}\mathrm{er}\:\mathrm{thank}\:\mathrm{you} \\ $$