यदि `x=2+2^(1//3)+2^(2//3)` है तो `x^(3)-6x^(2)+6x` का मान क्या है ?

Options

A. 1
B. 2
C. 3
D. `-2`

Answer

B

Explanation

दिया है, `x-2=2^(1//3)(1+2^(1//3))` . . .(i)
`rArr" "(x-2)^(3)=2(1+2^(1//3))^(3)`
`rArr" "x^(3)-8-6x^(2)+12x`
`=2(1+2+3*2^(1//3)+3*2^(2//3))`
`:." "x^(3)-6x^(2)+6x`
`=14+6*2^(1//3)+6*2^(2//3)-6x`
`=14+6*2^(1//3)+6*2^(2//3)`
`-6(2+2^(1//3)+2^(2//3))=2` [समी (i) से]