let-x-y-z-be-positive-real-number-such-that-x-4-y-4-z-4-1-find-the-minimum-value-of-x-3-1-x-8-y-3-1-y-8-z-3-1-z-8-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 192039 by universe last updated on 06/May/23

let x,y,z be positive real number such that x^4 +y^4 +z^4 = 1 find the minimum value of (x^3 /(1−x^8 )) + (y^3 /(1−y^8 )) + (z^3 /(1−z^8 ))

$$\mathrm{let}\:{x},{y},{z}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} \:=\:\mathrm{1}\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value} \\ $$$$\mathrm{of} \\ $$$$\:\:\:\:\frac{{x}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{8}} }\:+\:\frac{{y}^{\mathrm{3}} }{\mathrm{1}−{y}^{\mathrm{8}} }\:+\:\frac{{z}^{\mathrm{3}} }{\mathrm{1}−{z}^{\mathrm{8}} } \\ $$

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let-x-y-z-be-positive-real-number-such-that-x-4-y-4-z-4-1-find-the-minimum-value-of-x-3-1-x-8-y-3-1-y-8-z-3-1-z-8-

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