knowing-that-x-y-1-what-is-the-result-of-y-x-x-y-

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 \dots

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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