Question

If a-b=3 and b-c = 5, then the value of a2+b2+c2- ab-bc-ca is

Answer 1

a-b=3----(1)
b-c=5-----(2)

(1)+(2)

a-b+b-c=8
a-c=8

(a-b)^2=a^2+b^2-2ab
9=a^2+b^2-2ab-----(A)

(b-c)^2=b^2+c^2-2bc
25=b^2+c^2-2bc------(B)

(a-c)^2=a^2+c^2-2ac
64=a^2+c^2-2ac-------(C)

(A)+(B)+(C)
9+25+64=2(a^2+b^2+c^2-ab-bc-ca)
98=2(a^2+b^2+c^2-ab-bc-ca)
a^2+b^2+c^2-ab-bc-ca=49