Question

已知a=m+1,b=m+2,c=m+3 求a平方+b平方+c平方-ab-bc-ca

Answer 1

1)

a^2 + b^2 + c^2 - ab - bc - ca

= 1/2 * (2a^2 + 2b^2 + 2c^2 - 2ab - 2bc - 2ca)

= 1/2 * { (a-b)^2 + (b-c)^2 + (c-a)^2 }

= 1/2 * { (-1)^2 + (-1)^2 + 2^2 }

= 1/2 * 6

= 3

2)

a平方+b平方+c平方=ab+bc+ca

a^2 + b^2 + c^2 - ab - bc - ca = 0

2a^2 + 2b^2 + 2c^2 - 2ab - 2bc - 2ca = 0

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

a-b=0 ,b-c=0 ,c-a=0

a,b,c之间的关系 :a=b=c