Example 5. In right $\triangle \mathrm{ABC}$, $\angle \mathrm{C}=90^{\circ}$. What is the relationship between $\mathrm{d}^{3}+\mathrm{b}^{3}$ and $\mathrm{c}^{3}$?
In the right-angled $\triangle \mathrm{ABC}$, there is $\mathrm{a}^{2}+\mathrm{b}^{2}=\mathrm{c}^{2}$.
Multiplying both sides of the above equation by $c$ yields $a^{2} c+b^{2} c=c^{2} s$.
Expressing $c$ in terms of $a$ and $b$ ($c>a, c>b$), we get from $a^{2} c+$ $b^{2} c=c^{3}$ that
$$
a^{3}+b^{3}<c^{3} .
$$