a²+b²+c²=ab+bc+ac

a²+b²+c²=ab+bc+ac

2(a² + b² + c²)=2(ab + bc + ac)

a² -2ab+ b² + b² - 2bc + c² + a² -2ac + c² = 0

(a - b)² + (b - c)² +(a - c)² = 0

a = b,b = c, a = c

所以 a = b = c

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

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

在实数范围内a=b=c

a=b=c
移项并配方即可