If `x=2+2^(2/3)+2^(1/3)`, then the value of `x^3-6x^2+6x` is:

Options

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

Answer

B

Explanation

Let ` x = 2+2^(1//3) + 2 ^(2//3)`
` = 2 + 2 ^(1//3) + (2^(1//3))^(2) = 2 + 2 ^(1//3) (1+2^(1//3))`
` rArr x - 2 = 2 ^(1//3) ( 1 + 2 ^(1//3))`
On cubing both sides , we get
` x^(3) - 8 - 6x^(2) + 12x = 2 ( 1+2+3.2^(1//3)+3.2^(2//3))`
` rArr 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`