Question

if a+b+c=0,then a3+b3+c3 is equal to​

Answer 1

Answer:

, a3+b3 + c3 = (a+ b + c) (a2 + b2 + c2 – ab – be – ca) + 3abc

[using identity, a3+b3 + c3 – 3 abc = (a + b + c)(a2+b2+c2 –ab–bc-ca)] = 0 + 3abc [∴ a + b + c = 0]

a3+b3 + c3 = 3abc. 

Answer 2

Given:

$a+b+c=0.$

To find:

Value of $a^3+b^3+c^3$

Solution:

If $a+b+c=0$, then value of $a^3+b^3+c^3 \hspace{0.1cm} is \hspace{0.1cm} 3abc.$

We can solve the above mathematical problem using the following mathematical approach.

On transferring 'c' to RHS of the given equation, we get:

$a+b+c=0 \\ a+b=-c \\\\Cubing on both sides, we get \\\\ (a+b)^{3}=-c^{3} \\\\ a^{3}+b^{3}+3 a b(a+b)=-c^{3} \\\\ a^{3}+b^{3}+3 a b(-c)=-c^{3} \\\\ a^{3}+b^{3}-3 a b c=-c^{3} \\\\ a^{3}+b^{3}+c^{3}=3 a b c$

Therefore, $a^{3}+b^{3}+c^{3}$ is equal to $3abc.$