Question

If (x + 1/x) = √3 , then what is the value of x³¹⁸ + x³¹² + x²⁶⁶ + x²⁶⁰ + x⁶ + 1 ?
1. 1
2. 0
3. 1/√ 3
4. 1/3

Answer 1

Correct Answer - Option 2 : 0

Given:

(x + 1/x) = √3

Concept Used:

If (x + 1/x) = √3, then x⁶ = -1

Calculation:

x³¹⁸ + x³¹² + x²⁶⁶ + x²⁶⁰ + x⁶ + 1

⇒ x³¹²(x⁶ + 1) + x²⁶⁰(x⁶ + 1) + (x⁶ + 1)

⇒ (x³¹² + x²⁶⁰ + 1) × (x⁶ + 1)

⇒ (x³¹² + x²⁶⁰ + 1) × 0 = 0

∴ the required value is 0