21. Let $x_{1}$ and $x_{2}$ be two real numbers that satisfy $x_{1} x_{2}=2013$. What is the minimum value of $\left(x_{1}+x_{2}\right)^{2}$ ?
21. Answer: 8052
$$
\left(x_{1}+x_{2}\right)^{2}=\left(x_{1}-x_{2}\right)^{2}+4 x_{1} x_{2} \geq 0+4 \times 2013=8052 \text {. }
$$

If $x_{1}=x_{2}=\sqrt{2013}$, then $\left(x_{1}+x_{2}\right)^{2}=8052$.