Option 3 : 198

**Given:**

x + 1/x = 2√2

**Formula used:**

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

(a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)

**Calculation:**

x + 1/x = 2√2

Taking square on both sides,

x^{2} + 1/x^{2} + 2 = (2√2)^{2}

⇒ x2 + 1/x2 + 2 = 8

⇒ x2 + 1/x2 = 6

Taking cube on the both sides,

x^{6} + 1/x^{6} + 3 × x^{2} × 1/x^{2}(x2 + 1/x^{2}) = 216

⇒ x6 + 1/x^{6} = 216 - 18

⇒ x6 + 1/x6 = 198

**∴ The value of is x6 + 1/x ^{6} is 198.**

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