Question 83
$$
\max\{x^2+3x+3, x^{2011}+x^4+x^2+x+1\} \le \min\{1-x-x^2, x^{2011}+x^4+x^2+x+1\},
$$
where $\max\{a,b\} = \begin{cases} a, & \text{if } a \ge b \\ b, & \text{if } a \lt b \end{cases}$, and $\min\{a,b\} = \begin{cases} b, & \text{if } a \ge b \\ a, & \text{if } a \lt b \end{cases}$.
\max\{x^2+3x+3, x^{2011}+x^4+x^2+x+1\} \le \min\{1-x-x^2, x^{2011}+x^4+x^2+x+1\},
$$
where $\max\{a,b\} = \begin{cases} a, & \text{if } a \ge b \\ b, & \text{if } a \lt b \end{cases}$, and $\min\{a,b\} = \begin{cases} b, & \text{if } a \ge b \\ a, & \text{if } a \lt b \end{cases}$.