△=(2A-2C)^2-4*2*[(A-B)^2+(B-C)^2]
=4A^2+4C^2-8AC-8*(A^2-2AB+2B^2-2BC+C^2)
=4A^2+4C^2-8AC-8A^2+16AB-16B^2+16BC-8C^2
=-4A^2-4C^2-8AC+16AB-16B^2+16BC=0
A^2+C^2+2AC-4AB+4B^2-4BC=0
(A+C)^2-4B(A+C)+4B^2=0
(A+C-2B)^2=0
A+C-2B=0
A+C=2B
得证