If a1/3 + b1/3 + c1/3 = 0, then a relation among a, b ,

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If a^1/3 + b^1/3 + c^1/3 = 0, then a relation among a, b , c is

1. a + b + c = 0
2. (a + b + c)³ = 27abc
3. a + b + c = 3abc
4. a³ + b³ + c³ = 0

Correct Option: B

If a + b + c = 0
a³ + b³ + c³ = 3abc
∴ If a^1/3 + b^1/3 + c^1/3 = 0
⇒ (a^1/3)³ + (b^1/3)³ + (c^1/3)³
= 3.a^1/3.b^1/3.c^1/3
⇒ a + b + c = 3.a^1/3.b^1/3.c^1/3
⇒ (a + b + c)³
= 3³.(a^1/3.b^1/3.c^1/3)³ = 27abc