If $x = \sqrt[3]{5} + 2 $, then the value of $x^3 = 6x^2 + 12 x- 12$ is equal to:
Answer & explanation
Correct answer: option 3
(a - b)3 = a3 - b3 - 3ab(a-b)
If $x = \sqrt[3]{5} + 2 $,
then the value of $x^3 = 6x^2 + 12 x- 12$
If $x = \sqrt[3]{5} + 2 $
= x - 2 = $ \sqrt[3]{5}$
= (x - 2)3 = 5
x3 - 6x2 + 12x - 8 = 5
⇒ x3 - 6x2 + 12x - 13 = 0
⇒ x3 - 6x2 + 12x - 13 + 1 = 1
⇒ x3 - 6x2 + 12x - 12 = 1