问题
填空题
如果a=2003x+2001，b=2003x+2002，c=2003x+2003，那么代数式a2+b2+c2-ab-ac-bc的值等于______．
答案
∵a=2003x+2001，b=2003x+2002，c=2003x+2003
∴a-b=-1，b-c=-1，a-c=-2
∴a2+b2+c2-ab-ac-bc
=
(2a2+2b2+2c2-2ab-2ac-2bc )1 2
=
[(a2-2ab+b2)+(b2-2bc+c2)+(a2-2ac+c2)]1 2
=
[(a-b)2+(b-c)2+(a-c)2]1 2
=
(1+1+4)1 2
=3
故答案为3