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