Question

$\sqrt{x \div y} = 4 \: \: \:1 \div x + 1 \div y = 1 = xy$

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Answer 1

Simplify:

Step-by-step explanation:

$\ Given \ value:\\\\\sqrt{x\div y} \ = 4 \ \ \ and \ \ 1 \div x \ + \ 1 \div y = 1\div xy \\\\\ find : \\\\x=? \ \ \ \ and \ \ \ y =? \\\\\ Solution: \\\\\sqrt{x\div y} = 4.....(i)\\\\\ Square \ of \ the \ above \ equation: \\\\\rightarrow (\sqrt{x\div y})^2 = (4)^2 \\\\\rightarrow (\sqrt{\frac{x}{y}})^2 = (4)^2 \\\\\rightarrow \frac{x}{y} = 16 \\\\\rightarrow x = 16y.......(ii)$

$\rightarrow \frac{1}{x} + \frac{1}{y} = \frac{1}{xy}\\\\ \rightarrow \frac{y+x}{xy}= \frac{1}{xy}\\\\ \rightarrow \frac{y+x}{1}= \frac{xy}{xy}\\\\\rightarrow y+x= 1\\\\\ put \ the \ of \ x \ in \ above \ equation \\\\ \rightarrow y+16y= 1\\\\\rightarrow 17y= 1\\\\\rightarrow y= \frac{1}{17}\\\\\ put \ the \ value \ of \ y \ in \ equation \ (ii)\\\\\ Equation: \\\\\rightarrow x= 16y \\\\\rightarrow x= 16 \times \frac{1}{17}\\\\\rightarrow x= \frac{16}{17}$

$\rightarrow \ x= \frac{16}{17} \ \ \ \ \ \ \ \ and \ \ \ \ \ \rightarrow y= \frac{1}{17}$

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