6
分析:根据a.c.b的值,分别求出a-b=-1,b-c=-1,c-a=2,c-b=1进而得出-a-b+2c的值,即可得出答案.
解答:∵
![](http://thumb.1010pic.com/pic5/latex/544597.png)
,
![](http://thumb.1010pic.com/pic5/latex/544598.png)
,
![](http://thumb.1010pic.com/pic5/latex/544599.png)
,
∴a-b=-1,b-c=-1,c-a=
![](http://thumb.1010pic.com/pic5/latex/23406.png)
x+2012-
![](http://thumb.1010pic.com/pic5/latex/23406.png)
x-2010=2,
c-b=
![](http://thumb.1010pic.com/pic5/latex/23406.png)
x+2012-
![](http://thumb.1010pic.com/pic5/latex/23406.png)
x-2011=1,
∴2(a
2+b
2+c
2-ab-bc-ac),
=2[a(a-b)+b(b-c)+c(c-a)],
=2(-a-b+2c),
=2[(c-a)+(c-b)],
=2×3,
=6,
故答案为:6.
点评:此题主要考查了因式分解的应用,根据题意正确的分解因式得出(-a-b+2c)的值是解决问题的关键.