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find-x-y-5-2x-2-y-4-4x-3y-4-2x-2-y-4-3x-2y-




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

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