Correct Answer - Option 3 : 6

**Given:**

x4 + x-4 = 1154

**Formula used:**

(a + b)^{2} = a^{2} + b^{2} + 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

⇒ (x^{2} + 1/x^{2})^{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**