Question

If a+b+c=0 then what is the value of a^3+b^3+c^3=0​

Answer 1

Answer:

If a + b + c = 0

Then,

a + b + c = 0

a + b = - c -- (I)

(a + b)^3 = (- c)^3

a^3 + b^3 + 3ab (a + b) = - c^3

from equation (I) a + b = - c

a^3 + b^3 + 3ab (- c) = - c^3

a^3 + b^3 - 3abc = - c^3

a^3 + b^3 + c^3 = 3abc

Hence,

a^3 + b^3 + c^3 ‘not equal’ 0

but,

a^3 + b^3 + c^3 ‘equal’ 3abc

Answer 2

$Since, a {}^{3} +b {}^{3} +c {}^{3} −3abc \\ (a+b+c)(a {}^{2} +b {}^{2} +c {}^{2} −bc−ca−ab) \\Given, a+b+c=0 \\∴a {}^{3} +b {}^{3} +c {}^{3} −3abc=0 \\∴a {}^{3} +b {}^{3} +c {}^{3} =3abc$