已知a-b=2,b-c=1代数式a2+b2+c2-ab-bc-ca的值为多少,

a-b=2
b-c=1
相加
a-c=3
a²+b²+c²-ab-bc-ac=
=(2a²+2b²+2c²-2ab-2bc-2ac)/2
=[(a²-2ab+b²)+(b²-2bc+c²)+(c²-2ac+a²)]/2
=[(a-b)²+(b-c)²+(a-c)²]/2
=[2²+1²+3²]/2
=(4+1+9)/2
=7