a=2012x+2013,b=2012x+2014,c=2012x+2015,求a^2+b^2+c^2-ab-bc-ca

a^2+b^2+c^2-ab-bc-ca
=1/2*(2a^2+2b^2+2c^2-2ab-2bc-2ca)
=1/2*(a^2-2ab+b^2+c^2-2ca+a^2+b^2-2bc+c^2)
=1/2*[(a-b)^2+(a-c)^2+(b-c)^2]
=1/2*[(2012x+2013-2012x-2014)^2+(2012x+2013-2012x-2015)^2+(2012x+2014-2012x-2015)^2]
=1/2*[(-1)^2+(-2)^2+(-1)^2]
=1/2*(1+4+1)
=3