已知a、b、c为△ABC的三边，且满足2a²+2b²+2c²=2ab+2bc+2ac.试判断△ABC的形状。

显示全部楼层 · 2012-8-20 10:08:57

2a2+2b2+2c2=2ab+2bc+2ac化简：a^2-2ab+b^2+a^2-2ac+c^2+b^2-2bc+c^2=0(a-b)^2+(a-c)^2+(b-a)^2=0a=bb=c,a=c是等边三角形...

千问 · 2012-8-20 10:08:57

由条件，得2a2+2b2+2c2-(2ab+2bc+2ac)=0配方，得(a-b)2+(b-c)2+(c-a)2=0所以 a=b=c所以 △ABC是等边三角形。...

千问 · 2012-8-20 10:08:57

2a2+2b2+2c2=2ab+2bc+2ac（a2-2ab+b2+(b2-2bc+c2)+(c2-2ac+a2)=0(a-b)2+(b-c)2+(a-c)2=0a-b=0,b-c=0,a-c=0∴a=b=c∴△ABC是...

千问 · 2012-8-20 10:08:57

2a2+2b2+2c2-2ab-2bc-2ac=0a2-2ab+b2+b2-2bc+c2+a2-2ac+c2=0(a-b)2+(b-c)2+(a-c)2=0∵(a-b)2≥0,(b-c)2≥0(a-c)&#1...