If x = ³√5 + 2 then the value of x³

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If x = ³√5 + 2 then the value of x³ – 6x² + 12x – 13 is

1. –1
2. 1
3. 2
4. 0

Correct Option: D

x = ³√5 + 2
⇒ x - 2 = ³√5
Cubing on both sides ,
⇒ x³ - 3x² × 2 + 3x.(-2)² - 2³ = 5
⇒ x³ - 6x² + 12x - 8 = 5
⇒ x³ - 6x² + 12x - 8 - 5 = 0
⇒ x³ - 6x² + 12x - 13 = 0