Question

If x² + x + 1 = 0, then find the value of x⁸ + 1/x¹⁴
1. -3
2. -1
3. -2
4. 0

Answer 1

Correct Answer - Option 2 : -1

Given:

x2 + x + 1 = 0

Formula used:

If x + 1/x = -1 then x³ = 1

Calculation:

x2 + x + 1 = 0

Dividing both side of the equation by x, we get

⇒ x + 1 + 1/x = 0

⇒ x + 1/x = -1

So, x³ = 1

Now, x8 + 1/x14 

⇒ (x⁹/x) + (x/x¹⁵)

⇒ (x³)³/x + x/(x³)⁵

⇒ (1)³/x + x/(1)⁵

⇒ (1/x) + x

⇒ x + 1/x

⇒ -1

∴ The value of x8 + 1/x14 is -1.