Subject (1). Determine the rational numbers $x$ and $y$ that satisfy

$$
\sqrt{\frac{2}{3}}=\frac{(|2 x+y|-5) \cdot \sqrt{5}+\sqrt{2}}{|3 y-3| \cdot \sqrt{5}+\sqrt{3}}
$$[^2]
Solution. Multiplying the "means and extremes", $|3 y-3| \sqrt{2}=(|2 x+y|-5) \sqrt{3}$. From considerations of rationality, it follows that $|3 y-3|=0=|2 x+y|-5$, from which $(x, y) \in\{(-3,1),(2,1)\}$.

At least here the rationality of the numbers is actually relevant; see the next problem. What are children to believe, at this stage still "of the masses", when conditions from the statement are sometimes relevant, and sometimes not?