已知△ABC的三边长分别为a,b,c,周长为6,且a^2+b^2+c^2=ab+bc+ca,则△ABC的三边长分别为?

题目

已知△ABC的三边长分别为a,b,c,周长为6,且a^2+b^2+c^2=ab+bc+ca,则△ABC的三边长分别为?

答案

a^2+b^2+c^2=ab+bc+ca
=>2a²+2b²+2c²-2ab-2ac-2ca=0
=>(a-b)²+(b-c)²+(c-a)²=0
=>a=b,b=c,c=a
=>a=b=c,a+b+c=6
=>a=b=c=2