Question

If a^1/3 + b^1/3 + c ^1/3 =0
Then choose correct option
(1). a+b+c=0
(2). (a+b+c)³ =27abc
(3). a+b+c=3abc
(4). a³+b³ +c³ =0
Plz explain completely
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Answer 1

a1/3+ b 1/3 + c 1/3 = 0

= ( a1/3 + b1/3) = -c1/3

=( a1/3 + b1/3)3 = ( - c1/3 )3

= ( a1/3 )3 + ( b 1/3)3 + 3 a1/3 . b.1/3 ( a 1/3 + b1/3) = - c

= a + b + c + 3 a 1/3 b 1/3 ( - c 1/3 ) = 0

= ( a + b + c ) = 3 a 1/3 b 1/3 c 1/3

= ( a + b + c )3 = ( 3 a 1/3 b 1/3 c 1/3) 3

=( a + b + c )3 = 27 abc

therefore the correct answer is ( b )