Question Number 145772 by mathdanisur last updated on 07/Jul/21
$${a};{b};{c}>\mathrm{0}\:;\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{2}\:{prove}: \\ $$$$\left({a}^{\mathrm{6}} +{b}^{\mathrm{6}} +{c}^{\mathrm{6}} \right)^{\mathrm{3}} \:\geqslant\:\left({a}^{\mathrm{5}} +{b}^{\mathrm{5}} +{c}^{\mathrm{5}} \right)^{\mathrm{4}} \\ $$