If x = 2 - 21 / 3 + 22 / 3, then the value of x3

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If x = 2 - 2^{1 / 3} + 2^{2 / 3}, then the value of x³– 6x² + 18x + 18 is

1. 22
2. 33
3. 40
4. 45

Correct Option: C

x = 2 - 2^{1 / 3} + 2^{2 / 3}
⇒ x – 2 = 2^{2 / 3} - 2^{1 / 3}
On cubing both sides ,
⇒ x³ - 3x² × 2 + 3x × 4 – 8 = ( 2^{2 / 3} )³ - ( 2^{1 / 3} )³ - 3 . 2^{2 / 3} . 2^{1 / 3}( 2^{2 / 3} - 2^{1 / 3} )
⇒ x³ - 6x² + 12x – 8 = = 4 – 2 – 6 (x – 2)
⇒ x³ - 6x² + 12x – 8 = = 2 – 6x + 12
⇒ x³ - 6x² + 18x + 18 = 2 + 12 + 8 + 18 = 40