If-x-y-x-y-y-x-1-x-x-gt-0-and-y-gt-0-then-Find-the-value-of-x-y-

Question Number 191529 by MATHEMATICSAM last updated on 25/Apr/23

If \frac{x - y}{x \sqrt{y} + y \sqrt{x}} = \frac{1}{\sqrt{x}}; (x > 0 and y > 0) then

Find the value of \frac{x}{y} .

Answered by mehdee42 last updated on 25/Apr/23

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

x - \sqrt{x y} = \sqrt{x y} \Rightarrow x = 2 \sqrt{x y} \Rightarrow \frac{x}{y} = 4 ✓

Answered by Rasheed.Sindhi last updated on 25/Apr/23

\frac{x - y}{x \sqrt{y} + y \sqrt{x}} = \frac{1}{\sqrt{x}}

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

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

\frac{(\sqrt{x} - \sqrt{y})}{\sqrt{y}} = 1

\sqrt{x} = 2 \sqrt{y}

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

\frac{x}{y} = 4