Question

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______．

Answer 1

∵a=2003x+2001，b=2003x+2002，c=2003x+2003
∴a-b=-1，b-c=-1，a-c=-2
∴a²+b²+c²-ab-ac-bc
=

1

2

(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)
=3
故答案为3