已知a-b=2+根3,b-c=2-根3,求a方+b方+c方-ab-ac-bc

a-b=2+√3,b-c=2-√3
相加
a-c=4
a^2+b^2+c^2-ab-ac-bc
=(2a^2+2b^2+2c^2-2ab-2bc-2ca)/2
=[(a^2-2ab+b^2)+(b^2-2bc+c^2)+(c^2-2ca+a^2)]/2
=[(a-b)^2+(b-c)^2+(a-c)^2]/2
=[(2+√3)^2+(2-√3)^2+4^2]/2
=(4+4√3+3+4-4√3+3+16)/2
=30/2
=15