9.2. Is the number

$$
\sqrt[3]{2016^{2}+2016 \cdot 2017+2017^{2}+2016^{3}}
$$

- rational or irrational?
Answer: the whole rational number 2017. Solution. Let $a=2017, b=2016$. Then $b^{2}+a b+a^{2}+b^{3}=\frac{a^{3}-b^{3}}{a-b}+b^{3}=a^{3}-b^{3}+b^{3}=a^{3}$ (since $a-b=1$ ). Thus, we get $\sqrt[3]{a^{3}}=a=2017$