Question

已知A=2010X+2009,B=2010X+2010,C=2010X+2011,那么A2+B2+C2-AB-BC-AC

Answer 1

a-b=-1

b-c=-1

c-a=2

所以

a²+b²+c²-ab-bc-ac

=(2a²+2b²+2c²-2ab-2bc-2ac)/2

=[(a²-2ab+b²)+(b²-2bc+c²)+(c²-2ac+a²)]/2

=[(a-b)²+(b-c)²+(c-a)²]/2

=(1+1+4)/2

=3

选D