Question

已知a^2+b^2+c^2=ab+bc+ac,说明a=b=c

Answer 1

a^2+b^2+c^2=ab+bc+ac

两边同时乘以2

2(a^2+b^2+c^2)=2(ab+bc+ac)

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

(a-b)^2+(a-c)^2+(b-c)^2=0

a-b=0 a=b

a-c=0 a=c

c-b=0 c=b

∴a=b=c