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If x = \(\sqrt[3]{5} + 2\), then the value of x3 - 6x2 + 12x - 12 is equal to:

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Correct Answer - Option 3 : 1

Given 

x = \(\sqrt[3]{5} + 2\)

Formula Used

(a + b)3 = a3 + b3 + 3a2b + 3ab2

Calculation

⇒ x = ∛5 + 2 

⇒ x - 2 = ∛5  

⇒ (x- 2)3 = (∛5)3 

⇒ x3 - 6x2 + 12x - 8 = 5

⇒ x3 - 6x2 + 12x - 13 = 0 

⇒ x3 - 6x2 + 12x - 13 + 1 = 1

⇒ x3 - 6x2 + 12x - 12 = 1  

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