Question : If $x = \sqrt[3]{5} + 2$, then the value of $x^3-6x^2+12x-13$ is:
Option 1: $–1$
Option 2: $1$
Option 3: $2$
Option 4: $0$
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Correct Answer: $0$
Solution :
$x = \sqrt[3]{3} + 2$
⇒ $x - 2 = \sqrt[3]{5}$
By cubing on both the sides,
$⇒x^3-6x^2+3x (-2)^2-2^3=5$ [since $(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$]
$⇒x^3-6x^2+12x-8-5=0$
$⇒x^3-6x^2+12x-8-5=0$
$⇒x^3-6x^3+12x-13=0$
Hence, the correct answer is $0$.
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