Question

If x + 1/x = 3, then find x⁶ + 1/x⁶?
1. 343
2. 364
3. 322
4. 324

Answer 1

Correct Answer - Option 3 : 322

Given:

x + 1/x = 3

Formula used:

If x + 1/x = k

Then, x² + 1/x² = k² – 2

And, x³ + 1/x³ = k³ – 3k

Calculation:

x + 1/x = 3

Cube boht sides

⇒ x3 + 1/x3 = 33 – 3 × 3

⇒ x3 + 1/x3 = 27 – 9

⇒ x3 + 1/x3 = 18

Now, squar both sides

⇒ x⁶ + 1/x⁶ = 18² – 2

⇒ x6 + 1/x6 = 324 – 2

⇒ x6 + 1/x6 = 322

∴ Value of x⁶ + 1/x⁶ is 322.

Cubing first and then squaring will give the same answer as squaring first then cubing.