Question

if a +b+c=0 then find the value of x³+y³+z³​

Answer 1

Now, a3+b3 + c3 = (a+ b + c) (a2 + b2 + c2 – ab – be – ca) + 3abc

[using identity, a3+b3 + c3 – 3 abc = (a + b + c)(a2+b2+c2 –ab–bc-ca)] = 0 + 3abc [∴ a + b + c = 0]

a3+b3 + c3 = 3abc.

Answer 2

Given,

x +y +z = 0

Cubing both side,

(x +y +z)3 = 0

x3 + y3 + z3 -3xyz = 0[using formula]

x3 + y3 + z3 = 3xyz.