Question

a-b=3,b-c=4,求a的平方+b的平方+c的平方-ab-bc-ac

Answer 1

a-b=3,

b-c=4

两式相加得

a-c=7

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

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

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

=1/2[(a-b)^2+(b-c)^2+(a-c)^2]

=1/2*[3^2+4^2+7^2]

=1/2*(9+16+49)

=1/2*74

=37