SSC CGL 2022 PYQ — Question 81

The correct answer is option 1 i.e. $\frac{9}{4}$

x² - 3x + 1 = 0

x + 1/x = 3

On cubing both sides we get,

x³ + 1/x³ + 3(x + 1/x) = 27

x³ + 1/x³ = 27 - 9 = 18.

$\frac{(x^4+\frac{1}{x^2})}{(x^2+5x+1)}$.......(1)

Divide the N and D by x we get,

$\frac{(x^3+\frac{1}{x^3})}{(x+5+\frac{1}{x})}$ = (18)/(3 + 5) = 18/8 = 9/4.