Bjr
[tex]\dfrac{x}{y}+\dfrac{2y}{x}=3 \\\\\iff \dfrac{x^2+2y^2}{xy}=3\\\\\iff x^2+2y^2-3xy=0\\\\\iff (x-3y/2)^2-\dfrac{9y^2}{4}+2y^2=0\\\\\iff (x-3y/2)^2=\dfrac{y^2}{4}\\\\\iff x-3y/2=y/2 \ ou \ x-3y/2=-y/2\\\\\iff x=y \ ou \ x=2y[/tex]
Donc
[tex]E=\{(x,x);x\in \mathbb{N}^*\}\cup \{(x,2x);x\in \mathbb{N}^*\}[/tex]
Merci
