Question

If a + b +c =0 then what is the value of a ³ + b³ +c³=0?how to explain.

Answer 1

a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)
when,
a + b + c = 0

a³ + b³ + c³ - 3abc = 0
a³ + b³ + c³ = 3abc

or


(a+b+c)^3=(a^3+b^3+c^3)+3[(a+b+c)(ab+ac+bc)−abc]
if (a+b+c)=0
0=(a^3+b^3+c^3)+3(0*(ab+ac+bc)−abc)
0=(a^3+b^3+c^3)-3abc