​ If x = 3√(2 + √3), then x^3 + 1/x^3 = A. 2 B. 4 C. 8 D. 9 ​

Question

If x = \(\sqrt[3]{2+\sqrt3}\), then x³ + \(\frac{1}{x^3}\) =

A. 2

B. 4

C. 8

D. 9

Answer 1

Given x = \(\sqrt[3]{2+\sqrt3}\)

= x³ = 2 + √3

Similarly, \(\frac{1}{x^3}\) = 2 - √3

X³ + \(\frac{1}{x^3}\) = 2 +√3 + 2 - √3 = 4.