∀x,y∈R_+ ^∗ , show that (x/(x^4 +y^2 ))+(y/(y^4 +x^2 ))≤(1/(xy))


Question and Answers Forum

All Questions Topic List
Mensuration Questions
Previous in All Question Next in All Question
Previous in Mensuration Next in Mensuration
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

	$\frac{x}{x^{4} + y^{2}} + \frac{y}{x^{2} + y^{4}} ⩽ \frac{x}{2 x^{2} y} + \frac{y}{2 y^{2} x} = \frac{1}{2 x y} + \frac{1}{2 x y} = \frac{1}{x y}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum