Question

A cube plus b cube plus c cube minus 3 ABC find a + b + c is equals to 10 and a b + BC + CA is equals to 32

Answer 1

We are given, (a + b + c) = 10

        Squaring both sides,

  a^2 + b^2 + c^2 + 2ab + 2bc + 2ac = 100

a^2 + b^2 + c^2 +2(32) = 100

a^2 + b^2 + c^2 = 36 ...............................(1)

using the identity, a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2+b^2+c^2 - ab - bc - ac)

a^3 + b^3 + c^3 - 3abc = (10)(36 - 32) = 10(4) = 40