1)
a^2 + b^2 + c^2 - ab - bc - ca
= 1/2 * (2a^2 + 2b^2 + 2c^2 - 2ab - 2bc - 2ca)
= 1/2 * { (a-b)^2 + (b-c)^2 + (c-a)^2 }
= 1/2 * { (-1)^2 + (-1)^2 + 2^2 }
= 1/2 * 6
= 3
2)
a平方+b平方+c平方=ab+bc+ca
a^2 + b^2 + c^2 - ab - bc - ca = 0
2a^2 + 2b^2 + 2c^2 - 2ab - 2bc - 2ca = 0
(a-b)^2 + (b-c)^2 + (c-a)^2 = 0
a-b=0 ,b-c=0 ,c-a=0
a,b,c之间的关系 :a=b=c