Prove-that-3-2-1-5-3-1-5-5-1-5-gt-2-1-4-3-1-4-5-1-4-2-3-5-2-1-3-3-1-3-5-1-3-How-to-prove-it-

Question Number 7135 by Master Moon last updated on 12/Aug/16

Prove that (3/( (2)^(1/5) +(3)^(1/5) +(5)^(1/5) )) > (((2)^(1/4) +(3)^(1/4) +(5)^(1/4) )/(((√2)+(√3)+(√5))((2)^(1/3) +(3)^(1/3) +(5)^(1/3) ))) How to prove it ?

$$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\:\frac{\mathrm{3}}{\:\sqrt[{\mathrm{5}}]{\mathrm{2}}+\sqrt[{\mathrm{5}}]{\mathrm{3}}+\sqrt[{\mathrm{5}}]{\mathrm{5}}}\:>\:\frac{\sqrt[{\mathrm{4}}]{\mathrm{2}}+\sqrt[{\mathrm{4}}]{\mathrm{3}}+\sqrt[{\mathrm{4}}]{\mathrm{5}}}{\left(\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{5}}\right)\left(\sqrt[{\mathrm{3}}]{\mathrm{2}}+\sqrt[{\mathrm{3}}]{\mathrm{3}}+\sqrt[{\mathrm{3}}]{\mathrm{5}}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:{How}\:{to}\:{prove}\:{it}\:? \\ $$

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Prove-that-3-2-1-5-3-1-5-5-1-5-gt-2-1-4-3-1-4-5-1-4-2-3-5-2-1-3-3-1-3-5-1-3-How-to-prove-it-

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