Question

If a+b+c =0 then a^(5 )+b^5+c^5 = ?

Answer 1

Step-by-step explanation:

given,

a+b+c=0

then a^5+b^5+c^5=0^5

=0

hope it helps...

Answer 2

Answer:

Step-by-step explanation:

a + b + c = 0 so c = -(a + b).

a^5 + b^5 + c^5

= a^5 + b^5 - (a + b)^5..... (1)

By binomial theorem,

(a + b)^5 = a^5 + 5a^4*b + 10a^3*b^2 + 10a^2*b^3 + 5ab^4 + b^5.a^5 + b^5 + c^5

=-5ab (a^3 + 2a^2*b + 2ab^2 + b^3).

= -5ab (a^3 + b^3 + 2a^2*b + 2ab^2)

= -5ab [ (a + b)(a^2 -ab + b^2) + 2ab (a + b) ].

= -5ab (a + b) (a^2 + ab + b^2)