Question

if cube root a + cube root B plus cube root c is equals to zero then a + b + C whole cube is equals to​

Answer 1

Here, ∛a + ∛b + ∛c = 0

⇒ ∛a + ∛b = -∛c

By cubing both sides,

We get,

a + b + 3∛a ∛b ( ∛a + ∛b ) = c

a + b + 3∛a ∛b ( -∛c) = -c

a + b + c =  3∛a ∛b ( ∛c)

⇒ \frac{a+b+c}{3}=\sqrt[3]{a} \sqrt[3]{b} \sqrt[3]{c}3a+b+c=3a3b3c

By taking cube  on both sides,

⇒  ({\frac{a+b+c}{3}})^3=abc(3a+b+c)3=abc

Answer 2

Here, ∛a + ∛b + ∛c = 0

⇒ ∛a + ∛b = -∛c

By cubing both sides,

We get,

a + b + 3∛a ∛b ( ∛a + ∛b ) = c

a + b + 3∛a ∛b ( -∛c) = -c

a + b + c =  3∛a ∛b ( ∛c)

By taking cube  on both sides,

⇒  (a+b+c)^3=abc(3a+b+c)3=abc