Example 1. If $a$ and $b$ are real numbers, and
$$
\sqrt{2 a-1}+|b+1|=0 \text {. }
$$

Find the value of $a^{-2}+b^{-1987}$.
Solution: $\because \sqrt{2 a-1} \geqslant 0,|b+1| \geqslant 0$, according to property 5, we have
$$
\begin{array}{l}
\sqrt{2 a-1}=0 \text { and }|b+1|=0, \\
\therefore a=\frac{1}{2} \text { and } b=-1 \text {. Therefore, } \\
a^{-2}+b^{-1987}=\left(\frac{1}{2}\right)^{-2}+(-1)^{-1987} \\
=4-1=3 .
\end{array}
$$