1. Let $a-b=2+\sqrt{3}, b-c=2-\sqrt{3}$, then the value of $a^{2}+b^{2}+c^{2}$ $-a b-b c-c a$ is $\qquad$
1. 15

Let $S=a^{2}+b^{2}+c^{2}-a b-b c-c a$, then
$$
\begin{aligned}
2 S & =2 a^{2}+2 b^{2}+2 c^{2}-2 a b-2 b c-2 c a \\
& =(a-b)^{2}+(b-c)^{2}+(c-a)^{2} \\
& =(2+\sqrt{3})^{2}+(2-\sqrt{3})^{2}+4^{2} \\
& =30 .
\end{aligned}
$$
$$
\therefore \quad S=\frac{1}{2} \times 30=15 \text {. }
$$

That is, $a^{2}+b^{2}+c^{2}-a b-b c-c a=15$.