If-xyz-R-xyz-1-prove-that-the-following-inequality-holds-x-2x-5-x-4-y-2y-5-y-4-z-2z-5-z-4-3-7-Solution-please-with-an-advice-to-get-better-at-inequalities-and-which-book-wou

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Question Number 201859 by York12 last updated on 14/Dec/23

$$\mathrm{If}xyz\in {\mathbb{R}}^{+},xyz=1,\mathrm{prove}\mathrm{that}\mathrm{the}\mathrm{following}\mathrm{inequality}\mathrm{holds}:$$$$\frac{x}{2x^5+x+4}+\frac{y}{2y^5+y+4}+\frac{z}{2z^5+z+4}⩾\frac{3}{7}.$$$$\mathbf{Solution}\mathbf{please}\mathbf{with}\mathbf{an}\mathbf{advice}\mathbf{to}\mathbf{get}\mathbf{better}$$$$\mathbf{at}\mathbf{inequalities}\mathbf{and}\mathbf{which}\mathbf{book}\mathbf{would}\mathbf{you}\mathbf{recommend}.$$$$\mathbf{Thanks}\mathbf{in}\mathbf{advance}!$$$$$$

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