a2+2b2+2ab+2c+1=2bc+2a2 求 a,b,c

问题描述:

a2+2b2+2ab+2c+1=2bc+2a2 求 a,b,c

题目不对a²+2b²+2ab+2c+1=2bc-2c²则(a²+2ab+b²)+(b²-2bc+c²)+(c²+2c+1)=0(a+b)²+(b-c)²+(c+1)²=0所以a+b=0,b-c=0,c+1=0所以a=1,b=-1,c=-1