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If-x-y-are-real-numbers-satisfy-x-40-y-569-xy-26-y-x-then-xy-




Question Number 189919 by horsebrand11 last updated on 24/Mar/23
 If x,y are real numbers satisfy   ((x+40)/y)+((569)/(xy))=((26−y)/x) , then xy=?
$$\:{If}\:{x},{y}\:{are}\:{real}\:{numbers}\:{satisfy} \\ $$$$\:\frac{{x}+\mathrm{40}}{{y}}+\frac{\mathrm{569}}{{xy}}=\frac{\mathrm{26}−{y}}{{x}}\:,\:{then}\:{xy}=? \\ $$
Answered by cortano12 last updated on 24/Mar/23
⇒(x+20)^2 +(y−13)^2 =0  ⇒ { ((x=−20)),((y=13)) :}⇒xy=−260
$$\Rightarrow\left(\mathrm{x}+\mathrm{20}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{13}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$$\Rightarrow\begin{cases}{\mathrm{x}=−\mathrm{20}}\\{\mathrm{y}=\mathrm{13}}\end{cases}\Rightarrow\mathrm{xy}=−\mathrm{260} \\ $$

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