△ABC三边a,b,c满足a²+b²+c²=ab+bc+ca,试判定△ABC的形状.
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△ABC三边a,b,c满足a²+b²+c²=ab+bc+ca,试判定△ABC的形状.
△ABC三边a,b,c满足a²+b²+c²=ab+bc+ca,试判定△ABC的形状.
△ABC三边a,b,c满足a²+b²+c²=ab+bc+ca,试判定△ABC的形状.
a²+b²+c²=ab+bc+ca
2(a²+b²+c²)=2(ab+bc+ca)
2(a²+b²+c²)-2(ab+bc+ca)=0
(a-b)²+(a-c)²+(b-c)²=0
a-b=a-c=b-c=0
a=b=c
1/2(a²-2ab+b²+b²-2bc+c²+c²-2ac+a²)=0
1/2[(a-b)²+(b-c)²+(c-a)²]=0
故a=b=c,即△ABC是等边三角形