Question

tell me the correct answer

Answer 1

Opt. D) a3+b3+c3 = 0

Answer 2

We know that if a + b + c = 0, then a^3 + b^3 + c^3 = 3abc ------ (1)

Given Equation is a^(1/3) + b^(1/3) + c^(1/3) = 0 ----- (2)

Equation (2) is in the form of (1) , we can write it as,

$= > (a^\frac{1}{3})^3 + (b^\frac{1}{3})^3 + (c^\frac{1}{3})^3 = 3 * a^\frac{1}{3} * b^\frac{1}{3} * c^\frac{1}{3}$

$= > a + b + c = (3abc)^\frac{1}{3}$

Now,

On cubing both sides, we get

$= > (a + b + c)^3 = [3(abc)^\frac{1}{3}]^3$

$= > (a + b + c)^3 = 3^3 * (abc)^{\frac{1}{3} * 3}$

$= > \boxed{(a + b + c)^3 = 27abc}}$

----------------------------------------------------------------------------------------------------------------

Therefore, the correct answer is Option (C).

Hope this helps!