(a + b + c)² = 3ab + 3bc + 3ac
a² + b² + c² + 2ab + 2bc + 2ac = 3ab + 3bc + 3ac
a² + b² + c² - ab - bc - ac = 0
2a² + 2b² + 2c² - 2ab - 2bc - 2ac = 0
a² - 2ab + b² + b² - 2bc + c² + a² - 2ac + c² = 0
(a - b)² + (b - c)² + (a - c)² = 0
因为一个数的平方大于等于0
所以只有当 a - b = 0 且 b - c = 0 且 a - c = 0 时等号成立
所以 a = b = c