实数a、b、c满足:a2+6b=-17,b2+8c=-23,c2+2a=14,则a+b+c=_.

问题描述:

实数a、b、c满足:a2+6b=-17,b2+8c=-23,c2+2a=14,则a+b+c=______.

∵a2+6b=-17,b2+8c=-23,c2+2a=14,∴a2+6b+b2+8c+c2+2a=-26,∴(a2+2a+1)+(b2+6b+9)+(c2+8c+16)=0,即(a+1)2+(b+3)2+(c+4)2=0,∴a+1=0,即a=-1;b+3=0,即b=-3;c+4=0,即c=-4;∴a+b+c=-8.故答案是...