x² - √3x - 1 = 0 হলে, x⁶ + 1/x⁶ এর মান কত?

x² - √3x - 1 = 0
or, x² - 1 = √3x
or, (x² - 1)/x = √3
or, x - 1/x = √3

x² + 1/x²
= (x - 1/x)² + 2.x.1/x
= (√3)2 + 2
= 5

x⁴ + 1/x⁴
= (x²)² + (1/x²)²
= (x² + 1/x²)² - 2.x².1/x²
= 5² - 2
= 23

(x² + 1/x²)(x⁴ + 1/x⁴) = x⁶ + 1/x⁶ + x² + 1/x²
or, x⁶ + 1/x⁶ = (x² + 1/x²)(x⁴ + 1/x⁴) - (x² + 1/x²) = 5 × 23 - 5 = 110