SSC CGL 2022 PYQ — Question 62

The correct answer is Option 3. i.e. 23.

According to the question,

x² - 5x + 1 = 0

Dividing both sides by x, we get

x - 5 + 1/x = 0

⇒ x + 1/x = 5........(1)

Now we know that if x + 1/x = a,

then x³ + 1/x³ = a³ - 3a.......(2)

Thus solving the given equation,

= $\dfrac{x^6 + x^4 +x^2 + 1}{5x^3}$

= 1/5 × (x³ + x + 1/x + 1/x³)   

= 1/5 × (5³ - 3 × 5 + 5)......................... by (1) and (2)

= 1/5 × (115)

= 23