If x + (1/x) = √3, then find the value of x^{546} + x ^{540} + x^{336} + x^{330} + x^{6} + 1 + 5.

- 3
- 5
- 7
- 9

Option 2 : 5

**Given:**

x + (1/x) = √3

**Formula used:**

If, a + (1/a) = √3 then a^{6} + 1 = 0

**Calculations:**

x^{546} + x ^{540} + x^{336} + x^{330} + x^{6} + 1 + 5

⇒ x^{540}(x^{6} + 1) + x^{330}(x^{6} + 1) + x^{6} + 1 + 5

⇒ 0 + 0 + 0 + 5 (x^{6} + 1 = 0)

⇒ 5

**∴ Correct answer will be option 2 **

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