证明:若3(a2+b2+c2)=(a+b+c)2,则a=b=c

问题描述:

证明:若3(a2+b2+c2)=(a+b+c)2,则a=b=c

a²+b²+c²+2ab+2bc+2ca=3a²+3b²+3c²2a²+2b²+2c²-2ab-2bc-2ac=0(a²-2ab+b²)+(b²-2bc+c²)+(c²-2ac+a²)=0(a-b)²+(b-c)²+(c-a)...