Question

If x⁴ + x^-4 = 1154 then the value of x + x^-1 is:
1. 5
2. 12
3. 6
4. 8

Answer 1

Correct Answer - Option 3 : 6

Given:

 x4 + x-4 = 1154

Formula used:

(a + b)² = a² + b² + 2ab 

Calculation:

x4 + x-4 = 1154

      or 

x4 + 1/x4 = 1154        (1) 

By adding 2 on both sides in equation (1)

⇒ x4 + 1/x4 + 2 = 1154 + 2  

⇒ (x² + 1/x²)² = 1156

⇒ (x2 + 1/x2) = √1156 = 34       (2)

By adding 2 on both sides in equation (2) 

⇒ (x2 + 1/x2 + 2) = 34 + 2 

⇒ (x + 1/x)² = 36

⇒ (x + 1/x) = √36 = 6

∴  x + x-1 = 6