Question

five full solution plz.

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

Answer 2

Given a + b + c = 0 ......... (1)

Identity,
a^3 + b^3 + c^3 = (a + b + c) (a^2 + b^2 + c^2 – ab – bc - ca) + 3abc

Take 3abc to left

a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 – ab – bc - ca) ........... ...............(2)

Subsitute the value a + b + c = 0 in (2) i. e; in
a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 – ab – bc - ca)

We get

a^3 + b^3 + c^3 - 3abc = (0) x (a^2 + b^2 + c^2 – ab – bc - ca)

= a^3 + b^3 + c^3 - 3abc = 0
= a^3 + b^3 + c^3  = 3abc

Therefore, a^3 + b^3 + c^3  not ZERO but it is 3abc