यदि `root(3)(a)+root(3)(b)=root(3)(c)` है तो `(a+b-c)^(3)+27abc` का साधारणीकृत मान क्या होगा?

Options

A. -1
B. 3
C. -3
D. 0

Answer

D

Explanation

`root(3)(a)+root(3)(b)=root(3)(c)`
Take cube both sides
`(root(3)(a)+root(3)(b))^(3)=(root(3)(c))^(3)`
`implies a+b+3a^(1/3)b^(1/3) (root(3)(a)+root(3)(b))=c`
`implies a+b+3a^(1/3)b^(1/3)c^(1/3)=c`
`implies a+b-c=-3a^(1/3)b^(1/3)c^(1/3)`
Again take cube both sides
`implies (a+b-c)^(3)=-27abc`
`implies(a+b-c)^(3)+27abc=0`
Alternate:
Put value of `a=0`
`b=1, c=1`
value of `(a+b-c)^(3)+27abc`
`=(0+1-1)^(3)+27x0xx1xx1=0`