If \(y + {{1} \over y} = 3\), then what is the value of \({{1} \over y^3} + y^3 + 2 \)?

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SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 3)
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  1. 24
  2. 18
  3. 20
  4. 29

Answer (Detailed Solution Below)

Option 3 : 20
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Detailed Solution

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Given:

\(y + {{1} \over y} = 3\)

Concept used:

(a + b)3 = a3 + b3 + 3ab(a + b)

Calculation:

\(y + {{1} \over y} = 3\)

⇒ \((y + {{1} \over y})^3 = 27\)

⇒ \(y^3 + {{1} \over y}^3 +3(y +\frac{1}{y})= 27\)

⇒ \(y^3 + {{1} \over y}^3 +3 \times 3= 27\)

⇒ \(y^3 + {{1} \over y}^3 +9= 27\)

⇒ \(y^3 + {{1} \over y}^3= 18\)

⇒ \({{1} \over y^3} + y^3 + 2 \) = 20

∴ The required answer is 20.

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