已知：a=½m-2n+1,b=½m-2n+3,c=½m-2n+2.求值:a方+b方+c方-ab-ac-bc.

已知：a=½m-2n+1,b=½m-2n+3,c=½m-2n+2.求值:a方+b方+c方-ab-ac-bc.
已知：a=½m-2n+1,b=½m-2n+3,c=½m-2n+2.求值:a方+b方+c方-ab-ac-bc.

已知：a=½m-2n+1,b=½m-2n+3,c=½m-2n+2.求值:a方+b方+c方-ab-ac-bc.
a-b=-2,b-c1,c-a=1
a方+b方+c方-ab-ac-bc
=(1/2)[a^2+b^2-2ab+b^2+c^2-2bc+c^2+a^2-2ac]
=((1/2)[(a-b)^2+(b-c)^2+(c-a)^2]
=(1/2)[4+1+1]
=(1/2)6=3
a方+b方+c方-ab-ac-bc的值为3.

a-b=-2,a-c=-1,b-c=1

a方+b方+c方-ab-ac-bc。
=1/2(2a^2+2b^2+2c^2-2ab-2ac-2bc)
=1/2[(a-b)^2+(a-c)^2+(b-c)^2]
=1/2(4+1+1)
=3

b=a+2 c=a+1
a²+b²+c²-ab-ac-bc= a²+(a+2)²+(a+1)²-a(a+2+a+1)-(a+1)(a+2)
=3

先求2a方+2b方+2c方-2ab-2ac-2bc=（a-b)^2+(a-c)^2+(b-c)^2=4+1+1=6
所以本题答案为3