if-x-y-1-2-y-x-and-2x-2-7-thin-faind-volue-of-x-y-

Question Number 172703 by mathlove last updated on 30/Jun/22

i f \sqrt{\frac{x}{y}} + \frac{1}{\sqrt{2}} = \sqrt{\frac{y}{x}} a n d 2 x^{2} = 7

t h i n f a i n d v o l u e o f x \cdot y = ?

Answered by Rasheed.Sindhi last updated on 30/Jun/22

\sqrt{\frac{x}{y}} + \frac{1}{\sqrt{2}} = \sqrt{\frac{y}{x}} a n d 2 x^{2} = 7; x y = ?

L e t \sqrt{\frac{x}{y}} = a ⩾ 0

\frac{1}{a} - a = \frac{1}{\sqrt{2}}

\sqrt{2} (1 - a^{2}) = a

\sqrt{2} a^{2} + a - \sqrt{2} = 0

a = \frac{- 1 \pm \sqrt{1 + 8}}{2 \sqrt{2}} = \frac{1}{\sqrt{2}}^{✓}, \frac{- 2}{\sqrt{2}} (r e j e c t e d)

\sqrt{\frac{x}{y}} = \frac{1}{\sqrt{2}} \Rightarrow \frac{x}{y} = \frac{1}{2} \Rightarrow y = 2 x

\Rightarrow x y = x . 2 x = 2 x^{2} = 7

Commented by mathlove last updated on 30/Jun/22

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