Question

If (x + 1/x) = 3 then find the value x⁶ + 1/x⁶ 
1. 330
2. 322
3. 344
4. 356
5. 388

Answer 1

Correct Answer - Option 2 : 322

Given:

(x + 1/x) = 3

Formula used:

(a + b)² = a² + b² + 2ab

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

(x + 1/x) = 3

Taking cube both side.

(x + 1/x)³ = 3³

⇒ x³ + (1/x)³ + 3x × (1/x) (x + 1/x) = 27

⇒ x3 + (1/x)3 + 3 × 3 = 27

⇒ x3 + (1/x)3 = 18

Squaring both side,

⇒ (x3 + (1/x)3)² = (18)²

⇒ x6 + 1/x6 + 2(x3 × (1/x)3) = 324

⇒ x6 + 1/x⁶ + 2 = 324

⇒ x6 + 1/x⁶ = 322

∴ The value x6 + 1/x⁶ is 322.