यदि `a^(1//3)+b^(1/3)+c^(1/3)=0` है तो निम्न में से `a,b,c` के बीच कौन सा संबंध सही है?

Options

A. `a+b+c=0`
B. `(a+b+b+c)^(3)=0`
C. `a+b+c=3abc`
D. `a^(3)+b^(3)+c^(3)=0`

Answer

B

Explanation

`a^(1/3)+b^(1/3)+c^(1/3)=0`
`implies a^(1/3)+b^(1/3)=-c^(1/3)`
Take cube on both sides
`(a^(1/3)+b^(1/3))^(3)=(-c^(1/3))^(3)`
`implies a+b+3a^(1/3)b^(1/3)(a^(1/3)+b^(1/3))=-c`
`implies a+b+3a^(1/3)b^(1/3)xx(-c^((+1)/3))=-c`
`implies a+b+c=3a^(1/3)b^(1/3)c^(1/3)`
again taking cube
`(a+b+c)^(3)=27abc`