knowing that x+y=1. what is the result of (y/x)+(x/y)


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Question Number 57585 by Mikael_Marshall last updated on 07/Apr/19

$k n o w i n g t h a t x + y = 1 . w h a t i s t h e r e s u l t o f \frac{y}{x} + \frac{x}{y}$
	Answered by tanmay.chaudhury50@gmail.com last updated on 08/Apr/19

	$\frac{x^{2} + y^{2}}{x y}$ $R = \frac{{(x + y)}^{2} - 2 x y}{x y}$ $R = \frac{{(x + y)}^{2}}{x y} - 2$ $\frac{x + y}{2} ⩾ \sqrt{x y}$ $\frac{{(x + y)}^{2}}{x y} ⩾ 4$ $R ⩾ 4 - 2$ $R ⩾ 2$
	Commented by tanmay.chaudhury50@gmail.com last updated on 08/Apr/19

	$o k s i r . . .$
	Commented by MJS last updated on 08/Apr/19

	$\frac{x + y}{2} ⩾ \sqrt{x y} only makes sense for x ⩾ 0 \land y ⩾ 0$
	Answered by MJS last updated on 07/Apr/19

	$y = 1 - x$ $\frac{1 - x}{x} + \frac{x}{1 - x} = \frac{1}{x (1 - x)} - 2$
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