SSC CHSL 2022 PYQ — Question 53

The correct answer is option 2 i.e. -717√2.

If x + 1/x = c then, x² + 1/x² = c² - 2

If x + 1/x = c then, x³ + 1/x³ = c³ - 3c

 $(x^5+\frac{1}{x^5})$ = $(x^2+\frac{1}{x^2})$$(x^3+\frac{1}{x^3})$ - $x+\frac{1}{x}$

$x+\frac{1}{x}=-3\sqrt{2},$

x² + 1/x² = (-3√2)² - 2x/x = 18 - 2 = 16

x³ + 1/x³ = (-3√2)³ - 3(-3√2) = - 54√2 + 9√2 = - 45√2 

$(x^5+\frac{1}{x^5})$ =  16(-45√2) - (-3√2) = -720√2 + 3√2 = -717√2