a+b+c=0
=> a^2+b^2+c^2+2ab+2ac+2bc=0
=> a^2+b^2+c^2 = -(2ab+2ac+2bc)

1/(a+1)+1/(b+2)+1/(c+3)=0
=>(b+2)(c+3)+(a+1)(c+3)+(a+1)(b+2)=0
=>bc+ac+ab+3c+4b+5a+11=0
=>(ab+ac+bc)=-11-3c-4b-5a (我这里错了，当成正11了！)

(a+1)^2+(b+2)^2+(c+3)^2=a^2+b^2+c^2+ 14+2a+4b+6c
=-(2ab+2ac+2bc)+ 14+2a+4b+6c
=-2(-11-3c-4b-5a)+ 14+2a+4b+6c
=22+6c+8b+10a + 14+2a+4b+6c
=36+ 12(a+b+c)=36+12*0=36