If \(\rm K+\frac{1}{K}=3\), then what is the value of \(\frac{1}{K^3}+K^3\)?

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SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 4)
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  1. 36
  2. 10
  3. 18
  4. 54

Answer (Detailed Solution Below)

Option 3 : 18
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Detailed Solution

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Given:

\(\rm K+\frac{1}{K}=3\)

Concept used:

If \(\rm a+\frac{1}{a}=b\)

Then,

\(a^3+\frac{1}{a^3} = b^3 - 3b\)

Calculation:

\(\frac{1}{K^3}+K^3\)

⇒ \((\rm K+\frac{1}{K})^3-3(\rm K+\frac{1}{K})\)

⇒ 33 - 3 × 3

⇒ 27 - 9

⇒ 18

∴ The required answer is 18.

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