Question

已知a-b=3,b-c=5,求:a的2次方+b的2次方+c的2次方-ab-ac-bc的值

Answer 1

a-c=a-b+b-c=3-5=8

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

=1/2{(a^2-2ab+b^2)+(a^2-2ac+c^2)+(b^2-2bc+c^2)}

=1/2{(a-b)^2+(a-c)^2+(b-c)^2}

=1/2(9+64+25)

=1/2x98

=49