x^{1/8} + x^{-1/8 }= 2, then find the value of x^{27} + x^{-27} + 2.

- 1
- 4
- 9
- 16

Option 2 : 4

**Given : **

x^{1/8} + x^{-1/8 }= 2

**Concept used :**

x^{a} + x^{-a} = 2, then x must be equal to 1

**Calculations :**

x^{1/8} + x^{-1/8 }= 2

Squaring both the sides, we get

x^{1/4} + x^{-1/4} = 2

Again squaring

x^{1/2} + x^{-1/2} = 2

Again squaring

x + x^{-1} = 2

Every time we get x = 1

So,

x^{27} + x^{-27} + 2 = 1 + 1 + 2

⇒ 4

**∴ **Option 2 will be the correct choice.

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