Question

已知a=2002x+2001,b=2002x+2002,c=2002x+2003,求a的平方+b的平方+c的平方—ab—

Answer 1

a=2002x+2001,b=2002x+2002,c=2002x+2003

∴a-b=-1,b-c=-1,c-a=2

∴a2+b2+c2-ab-ac-bc

=1/2[2a2+2b2+2c2-2ab-2ac-2bc]

=1/2[（a-b)^2+(b-c)^2+(c-a)^2]

=1/2[（-1)^2+(-1)^2+2^2]

=3