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Given : x = 3 - √8.
Now,
⇒ x + 1/x = 3 - √8 + 3 + √8
= 6.
Hence, x + 1/x = 6.
On cubing both sides, we get
⇒ (x + 1/x)^3 = (6)^3
⇒ x^3 + (1/x^3) + 3(x + 1/x) = 216
⇒ x^3 + (1/x^3) + 3(6) = 216
⇒ x^3 + (1/x^3) = 216 - 18
⇒ x^3 + 1/x^3 = 198.
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