If , then what is the value of ?

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 3)
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  1. 42
  2. 52
  3. 36
  4. 18

Answer (Detailed Solution Below)

Option 2 : 52
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Detailed Solution

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Given:

Concept used:

If 

Then,

Calculation:

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

Now,

 = 43 - 3 × 4

⇒  = 64 - 12

⇒  = 52

∴ Ther required answer is 52.

 Shortcut Trick

We know,

• If k4 + 1/k4  = a then k2 + 1/k2 = √(a + 2)

• If k2 + 1/k2 = b then k + 1/k = √(b + 2)

• If k + 1/k = c then k3 + 1/k3 = c3 - 3c

So, k4 + 1/k4 = 194 then  k2 + 1/k2 = √196 = 14 so, k + 1/k = √16 = 4

Then, k3 + 1/k3 = 43 - 12 = 52

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