SSC CHSL 2022 PYQ — Question 61

The correct answer is option 1 i.e. 536

Given:

 p⁴ = 4354 - $\frac{1}{p^4}$ 

Explanation:

According to the given question,

 p⁴ + $\frac{1}{p^4}$ = 4354

Adding 2 on both sides, we get

⇒ (p² + $\frac{1}{p^2}$)² = 4356

⇒ (p² + $\frac{1}{p^2}$) = 66

Now subtracting 2 from both sides, we get

⇒ (p - $\frac{1}{p}$)² = 64

⇒ (p - $\frac{1}{p}$) = 8

Now, (p - $\frac{1}{p}$)³ =  p³ - $\frac{1}{p^3}$ - 3(p - $\frac{1}{p}$)

⇒  p³ - $\frac{1}{p^3}$ - 3(8) = 512

⇒  p³ - $\frac{1}{p^3}$  = 512 + 24

⇒  p³ - $\frac{1}{p^3}$ = 536

Hence the required answer is 536.