Question 29
Suppose $\frac{1}{2} \leq x \leq 2$ and $\frac{4}{3} \leq y \leq \frac{3}{2}$. Determine the minimum value of
$$
\frac{x^{3} y^{3}}{x^{6}+3 x^{4} y^{2}+3 x^{3} y^{3}+3 x^{2} y^{4}+y^{6}}
$$
$$
\frac{x^{3} y^{3}}{x^{6}+3 x^{4} y^{2}+3 x^{3} y^{3}+3 x^{2} y^{4}+y^{6}}
$$