Question

Suppose that for some a,b,c we have a+b+c = 6, ab+ac+bc = 5 and abc = -12. What is a^3+b^3+c^3?

Answer 1

(a+b+c)^3 = a^3 + b^3 + c^3 + 3a^2b + 3a^2c + 3ab^2 + 3ac^2 + 3b^2c + 3bc^2 + 6abc
(a+b+c)(ab+ac+bc) = a^2b + a^2c + ab^2 + ac^2 + 3abc
so, that means that

(a+b+c)^3 - 3(a+b+c)(ab+ac+bc) = a^3 + b^3 + c^3 - 3abc
Now just plug in your numbers