If x⁴ - 83x² + 1 = 0, then a value of x³ - x^-3 can be:

A. 758

B. 756

C. 739

D. 737

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & {x^4} - 83{x^2} + 1 = 0 \cr & {x^2} - 83 + \frac{1}{{{x^2}}} = 0 \cr & {x^2} + \frac{1}{{{x^2}}} = 83 \cr & {x^2} + \frac{1}{{{x^2}}} - 2 = 83 - 2 \cr & {\left( {x - \frac{1}{x}} \right)^2} = 81 \cr & x - \frac{1}{x} = 9 \cr & {\left( {x - \frac{1}{x}} \right)^3} = {9^3} \cr & {x^3} - \frac{1}{{{x^3}}} - 3 \times 9 = 729 \cr & {x^3} - \frac{1}{{{x^3}}} = 756 \cr} $$