14
a^2+b^2+c^2=ab+bc+ca
2a^2+2b^2+2c^2=2ab+2bc+2ca
(a-b)^2+(c-a)^2+(b-c)^2=0
a=b=c; a+2b+3c=12
a=b=c=2,a+b^2+c^3=14.