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

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

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