If x,y are real numbers satisfy ((x+40)/y)+((569)/(xy))=((26−y)/x) , then xy=?


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Question Number 189919 by horsebrand11 last updated on 24/Mar/23

$I f x, y a r e r e a l n u m b e r s s a t i s f y$ $\frac{x + 40}{y} + \frac{569}{x y} = \frac{26 - y}{x}, t h e n x y = ?$
	Answered by cortano12 last updated on 24/Mar/23
	$⇒(x+20)^2 +(y−13)^2 =0 ⇒ { ((x=−20)),((y=13)) :}⇒xy=−260$
	$\Rightarrow {(x + 20)}^{2} + {(y - 13)}^{2} = 0$ $\Rightarrow {\begin{cases} x = - 20 \\ y = 13 \end{cases} \Rightarrow xy = - 260$
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