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Question Number 85854 by jagoll last updated on 25/Mar/20

$$\mathrm{If}\mathrm{x},\mathrm{y},\mathrm{z}\in \mathbb{R}\mathrm{satisfy}\mathrm{the}\mathrm{equation}$$$${\mathrm{x}}^4+{\mathrm{y}}^4+{\mathrm{z}}^4=4\mathrm{xyz}-1$$$$\mathrm{find}\mathrm{minimum}\mathrm{value}\mathrm{of}$$$$\mathrm{x}+\mathrm{y}+\mathrm{z}$$

Commented by mr W last updated on 25/Mar/20

$$seemstobe3$$

Commented by mr W last updated on 25/Mar/20

$$x=y=z=1fulfillsthesymmetryand$$$$x^4+y^4+z^4=4xyz-1$$$$\text{Missing left or extra right}$$

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