Question

已知a-b=4+√5,b-c=4-√5,求a方+b方+c方-ab-bc-ac的值

Answer 1

a-c=8

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

=(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+(c-a)^2]/2

=(16+5+16+5+64)/2

=53