SSC CGL 2020 PYQ — Question 54

The correct answer is option 2 i.e 322

Explanation:

x² - 3x + 1 = 0

Divide both sides by x,

x - 3 + 1/x = 0

x + 1/x = 3

On taking the cube in both sides,

(x + 1/x)³ = 3³

x³ + x^1/3 + 3(x + 1/x) = 27

(∵(a + b)³ = a³ + b³ + 3ab(a + b))

x³ + x^1/3 + 3(3) = 27

x³ + x^1/3 = 18

On taking square both sides,

(x³ + x^1/3)² = 18²

x⁶ + x^1/6 + 2 = 324

(∵(a + b)² = a² + b² + 2ab)

x⁶ + x^1/6 = 322