SSC CGL 2022 PYQ — Question 69

The correct answer is Option 2 i.e. 52.

Given:

$k^4+({{1} \over k^4})=194$

Formula used:

(a + b)² = a² + b² + 2ab

(a + b)² = a³ + b³ + 3ab(a + b)

Calculations:

Using equation (1), we get

⇒ (K² + 1/K²)² = K⁴ + 1/K⁴ + 2

⇒ (K² + 1/K²)² = 194 + 2

⇒ (K² + 1/K²) = 14

Similarly,

⇒ (K + 1/K)² = (K² + 1/K²) + 2

⇒ (K + 1/K)² = 14 + 2

⇒ (K + 1/K) = 4

Now, using equation (2), we get

⇒ (K³ + 1/K³) = (K + 1/K)³ - 3(K + 1/K)

⇒ (K³ + 1/K³) = 4³ - 3 × 4

⇒ (K³ + 1/K³) = 64 - 12 = 52