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Question Number 151496 by puissant last updated on 21/Aug/21

\forall x, y \in R_{+}^{*}, s h o w t h a t \frac{x}{x^{4} + y^{2}} + \frac{y}{y^{4} + x^{2}} ⩽ \frac{1}{x y}

Answered by dumitrel last updated on 21/Aug/21

\frac{x}{x^{4} + y^{2}} + \frac{y}{x^{2} + y^{4}} ⩽ \frac{x}{2 x^{2} y} + \frac{y}{2 y^{2} x} = \frac{1}{2 x y} + \frac{1}{2 x y} = \frac{1}{x y}

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