Question

初二数学，求解

Answer 1

两边同乘2得
2a²+2b²+2c²=2ab+2bc+2ac
把右边移到左边，可化为3个完全平方式（a-b）²+(a-c)²+(b-c)²=0
所以（a-b）=(a-c)=(b-c)=0

Answer 2

Answer 3

证明：∵a²+b²+c²=ab+bc+ca
∴2a²+2b²+2c²-2ab-2bc-2ca=0
∴(a²-2ab+b²)+(b²-2bc+c²)+(c²-2ca+a²)=0
∴(a-b)²+(b-c)²+(c-a)²=0
∴a-b=0且b-c=0且c-a=0
∴a=b且b=c且c=a
∴a=b=c

Answer 4

反证法，设a等于b等于c。然后就很简单啦。望采纳

Answer 5

a^2+b^2+c^2=ab+bc+ca
2a^2+2b^2+2c^2=2ab+2bc+2ca
(a^2+b^2)+(b^2+c^2)+(c^2+a^2)=2ab+2bc+2ca
(a^2-2ab+b^2)+(b^2-2bc+c^2)+(c^2-2ca+a^2)=0
(a-b)^2+(b-c)^2+(c-a)^2=0
a-b=b-c=c-a=0
a=b=c

追答

亲可以采纳吗～^ _ ^