Ta có:
$x^3+y^3=2x^2y^2$
$\Leftrightarrow \dfrac{x}{y^2}+\dfrac{y}{x^2}=2$
$\Rightarrow \left(\dfrac{x}{y^2}+\dfrac{y}{x^2}\right)^2=4$
$\Leftrightarrow \left(\dfrac{x}{y^2}+\dfrac{y}{x^2}\right)^2-\dfrac{4}{xy}=4-\dfrac{4}{xy}$
$\Leftrightarrow \left(\dfrac{x}{y^2}-\dfrac{y}{x^2}\right)^2=4\left(1-\dfrac{1}{xy}\right)$
$\Rightarrow \sqrt{1-\dfrac{1}{xy}}=\dfrac{1}{2}\left|\dfrac{x}{y^2}-\dfrac{y}{x^2}\right|$, đpcm.