Question

已知a^2+b^2+c^2-ab-bc-ca=0,请谁导出a=b=c.

Answer 1

等式两边同时乘2,得:

2a^2+2b^2+2c^2-2ab-2ac-2ca=0

整理,得:(a^2-2ab+b^2)+(b^2-2bc+c^2)+(a^2-2ca+c^2)=0

即(a-b)^2+(b-c)^2+(c-a)^2=0

所以a=b=c