2. Let $p$ be a positive real number. Among all pairs of positive real numbers $(x, y)$ that satisfy the equation $x y(x+y)=p$, find the one for which the value of the expression $x^{3}+y^{3}$ is the smallest.
II/2. Since $x^{3}+y^{3}-p=x^{3}+y^{3}-x^{2} y-x y^{2}=x^{2}(x-y)-y^{2}(x-y)=(x-y)^{2}(x+y) \geq 0$, the value of the expression is certainly greater than or equal to $p$. Equality is achieved only for $x=y=\left(\frac{p}{2}\right)^{\frac{1}{3}}$.