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a-b-c-gt-0-a-2-b-2-c-2-2-prove-a-6-b-6-c-6-3-a-5-b-5-c-5-4-




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

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