Question

If a+b+c=0 then evaluate a power 3 + b power 3 + c power 3

Answer 1

See,

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