Question

代数式2a²+2b²+2c²-2ab-2bc-2ac的值为0,则a,b,c的关系是?本人有

Answer 1

2a²+2b²+2c²-2ab-2bc-2ac=0 => (a²-2ab+b²)+(a²-2ac+c²)+(c²-2bc+b²)=0

(a-b)^2+(a-c)^2+(c-b)^2=0 三个完全平方（非负数）的和等于零的充分必要条件是它们分别等于零,所以(a-b)^2=0,(a-c)^2=0,(c-b)^2=0 => a-b=0,a-c=o,c-b=o

a=b=c ,即 a,b,c相等.