SSC CGL 2023 PYQ — Question 54

The correct answer is option 1 i.e. 15127

Given that

If a + $\frac{1}{a}$ = 7  .......(1

Squaring both sides

⇒ (a + $\frac{1}{a}$)² = 49 

⇒ a² + 1/a² + 2 = 49

⇒ a² + 1/a² = 47

Now, cube both sides of Equation 1

⇒ (a + $\frac{1}{a}$)³ = 343 

⇒ a³ + 1/a³ + 3(a + 1/a) = 343

⇒ a³ + 1/a³ + 3 × 7 = 343

⇒ a³ + 1/a³ = 343 - 21 = 322

Now, 

⇒ a⁵ + $\frac{1}{a^5}$  = (a³ + 1/a³) (a² + 1/a²) - (a + 1/a)

⇒ 322 × 47 - 7

⇒ 15134 - 7 = 15127