已知a=x^2+2011,b=x^2+2012,c=x^2+2013,求a^2+b^2+c^2-ab-bc-ca的值.

a=x^2+2011,b=x^2+2012,c=x^2+2013
∴a-b=-1
a-c=-2
b-c=-1
a^2+b^2+c^2-ab-bc-ca
=½﹙2a²+2b²+2c²-2ab-2ac-2bc)
=½[(a²-2ab+b²)+(a²-2ac+c²)+(b²-2bc+c²)]
=½[(a-b)²+(a-c)²+(b-c)²]
=½×[(-1)²+(-2)²+(-1)²]
=½×6
=3