If  and x > 1, what is the value of ?

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SSC CGL 2023 Tier-I Official Paper (Held On: 19 Jul 2023 Shift 1)
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  1. 140√2
  2. 116√2
  3. 144√2
  4. 128√2

Answer (Detailed Solution Below)

Option 1 : 140√2
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SSC CGL Tier 1 2025 Full Test - 01
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Detailed Solution

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Concept used:

• If (x + 1/x) = a then (x - 1/x) = √(a2 - 4)

• If x + 1/x = a, then (x3 + 1/x3) = a3 - 3a

• If x - 1/x = a, then (x3 - 1/x3) = a3 + 3a

Calculation:

, then  (x - 1/x) = √(8 - 4) = 2

⇒ (x3)2 - (1/x3)2

⇒ (x3 + 1/x3) (x3 - 1/x3)

⇒ [(2√2)3 - 3(2√2)] [23 + 3 × 2]

⇒ [16√2 - 6√2] × 14

⇒ 10√2 × 14

⇒ 140√2

∴ The correct answer is 140√2

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