If a^1/3+b^1/3+c^1/3=0, then which of the following expression is correct?
A)a+b+c=0
B)(a+b+c)^3=27abc
C) a+b+c=3abc
D)a^3+b^3+c^3=0
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a^1/3 + b^1/3 + c^1/3 =0
a^1/3 + b^1/3 = - c^1/3.................. (1)
TAKE a cube both sides
a + b +3a^1/3 b^1/3 (a^1/3 + b^1/3) = - c
a + b + c = - 3 a^1/3 b^1/3 ( a^1/3 + b^1/3)
From equation 1
a + b + C = 3 a^1/3 b^1/3 c^1/3
Again cubeing both sides
(A + b + C)^3 = 27
a^1/3 + b^1/3 = - c^1/3.................. (1)
TAKE a cube both sides
a + b +3a^1/3 b^1/3 (a^1/3 + b^1/3) = - c
a + b + c = - 3 a^1/3 b^1/3 ( a^1/3 + b^1/3)
From equation 1
a + b + C = 3 a^1/3 b^1/3 c^1/3
Again cubeing both sides
(A + b + C)^3 = 27
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