Question

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

Answer 1

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