Given A-B = 3, B-C = - 1, find the value of a ^ 2 + B ^ 2 + C ^ 2-ab-bc-ac | Math enthusiast | Mathematical art

Given A-B = 3, B-C = - 1, find the value of a ^ 2 + B ^ 2 + C ^ 2-ab-bc-ac

a-b=3,b-c=-1
a-c=2
a^2+b^2+c^2-ab-bc-ac
=1/2*2(a^2+b^2+c^2-ab-bc-ac)
=1/2（2a^2+2b^2+2c^2-2ab-2bc-2ac)
=1/2((a-b)^2+(b-c)^2+(a-c)^2)
=1/2*(9+1+4)
=7
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