Find the shortest distance from the origin to the curve xy=3


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Question Number 28198 by NECx last updated on 21/Jan/18

$F i n d t h e s h o r t e s t d i s t a n c e f r o m$ $t h e o r i g i n t o t h e c u r v e x y = 3$
	Answered by mrW2 last updated on 22/Jan/18

	$d i s t a n c e o f p o i n t (x, y) t o t h e o r i g i n i s r .$ $r^{2} = x^{2} + y^{2}$ $x y = 3$ $\Rightarrow r^{2} = x^{2} + \frac{9}{x^{2}} ⩾ 2 \sqrt{x^{2} \times \frac{9}{x^{2}}} = 6 (A M ⩾ G M)$ $\Rightarrow r_{m i n} = \sqrt{6}$
	Commented by math solver last updated on 22/Jan/18

	$n i c e!$
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