x,y,z ∈ R^+ x^2 + y^3 + z^4 = x^4 + y^5 + z^6 Prove that (x^2 /(y^4 +1)) + (y^2 /(z^4 +1)) + (z^2 /(x^4 +1)) ≥ ((x^2 +y^2 +z^2 )/2)


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Question Number 99513 by naka3546 last updated on 21/Jun/20

$x, y, z \in R^{+}$ $x^{2} + y^{3} + z^{4} = x^{4} + y^{5} + z^{6}$ $P r o v e t h a t$ $\frac{x^{2}}{y^{4} + 1} + \frac{y^{2}}{z^{4} + 1} + \frac{z^{2}}{x^{4} + 1} ⩾ \frac{x^{2} + y^{2} + z^{2}}{2}$
Commented by Rasheed.Sindhi last updated on 21/Jun/20

$You can't use 'macro parameter character #' in math mode$ $p l e a s e s a y w h e t h e r t h e a n s w e r$ $i s c o r r e c t o r i n c o r r e c t .$
Commented by naka3546 last updated on 22/Jun/20

$I h a v e c o n f i r m e d, s i r . {T h a t}^{'} s c o r r e c t .$
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