Question

已知a,b,c是△ABC的三边,且满足关系式a^2+c^2=2ab+2ac-2b^2,试判断△ABC的形状

Answer 1

题目是否有误,关系式是否应为a^2+c^2=2ab+2bc-2b^2?

a^2+c^2=2ab+2bc-2b^2

a^2-2ab+b^2+c^2-2bc+b^2=0

(a-b)^2+(c-b)^2=0

于是

a-b=0,c-b=0

a=b=c

△ABC为等边三角形.