Question Number 222659 by Mingma last updated on 03/Jul/25
Answered by mr W last updated on 04/Jul/25
Commented by mr W last updated on 04/Jul/25
$$\frac{\mathrm{10}}{\mathrm{3}+{x}+\mathrm{7}−{y}}=\frac{\mathrm{10}−{y}}{\mathrm{3}} \\ $$$$\left(\mathrm{10}−{y}\right)\left(\mathrm{10}−{y}+{x}\right)=\mathrm{30} \\ $$$$\Rightarrow\left(\mathrm{10}−{y}\right)^{\mathrm{2}} +{x}\left(\mathrm{10}−{y}\right)=\mathrm{30}\:\:\:…\left({i}\right) \\ $$$$\frac{\mathrm{7}}{{x}+\mathrm{3}+\mathrm{10}−{y}}=\frac{\mathrm{7}−{y}}{{x}} \\ $$$$\left(\mathrm{10}−{y}−\mathrm{3}\right)\left(\mathrm{10}−{y}+{x}+\mathrm{3}\right)=\mathrm{7}{x} \\ $$$$\Rightarrow\left(\mathrm{10}−{y}\right)^{\mathrm{2}} +{x}\left(\mathrm{10}−{y}\right)=\mathrm{10}{x}+\mathrm{9}\:\:\:…\left({ii}\right) \\ $$$$\mathrm{10}{x}+\mathrm{9}=\mathrm{30} \\ $$$$\Rightarrow{x}=\frac{\mathrm{21}}{\mathrm{10}}=\mathrm{2}.\mathrm{1}\:\checkmark \\ $$
Commented by Mingma last updated on 05/Jul/25
Perfect, sir!