Question

If a+b+c = 0 show that a^3 +b^3+c^3 = 3(b+c)(c+a)(a+b).
​

Answer 1

Answer:

a

3

+b

3

+c

3

=3abc

Step-by-step explanation:

We know,

a

3

+b

3

+c

3

−3abc=(a+b+c)(a

2

+b

2

+c

2

−ab−bc−ca)

Putting a+b+c=0 on RHS, we get,

a

3

+b

3

+c

3

−3abc=0

⟹a

3

+b

3

+c

3

=3abc, Hence proved.