Question

3(a二次方+b二次方+c二次方)=(a+b+c)的二次方,求证：a=b=c

Answer 1

3(a² + b² + c²) = (a + b + c)²

3a² + 3b² + 3c² = a² + b² + c² + 2ab + 2ac + 2bc

2a² + 2b² + 2c² - 2ab - 2ac - 2bc = 0

(a - b)² + (a - c)² + (b - c)² = 0

因为一个数的平方大于等于0

所以只有当 a - b = 0 ,a - c = 0 ,b - c = 0 的时候等号才成立

所以 a = b = c