Question Number 82031 by M±th+et£s last updated on 17/Feb/20
$${find}\:{x},{y} \\ $$$$\begin{cases}{\mathrm{5}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }\:=\mathrm{4}{x}−\mathrm{3}{y}}\\{\mathrm{4}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }\:=\mathrm{3}{x}−\mathrm{2}{y}}\end{cases} \\ $$
Answered by MJS last updated on 17/Feb/20
$$\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }=\frac{\mathrm{4}{x}−\mathrm{3}{y}}{\mathrm{5}}=\frac{\mathrm{3}{x}−\mathrm{2}{y}}{\mathrm{4}} \\ $$$$\Rightarrow \\ $$$${y}=\frac{{x}}{\mathrm{2}} \\ $$$$\Rightarrow\:{x}=\mathrm{0}\wedge{y}=\mathrm{0}\vee{x}=\mathrm{2}\sqrt{\mathrm{7}}\wedge{y}=\sqrt{\mathrm{7}} \\ $$