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if-a-b-c-gt-0-and-ab-bc-ca-2-then-cyc-a-b-4-c-4-b-3-b-2-c-bc-2-c-3-1-




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

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