1.

If x + (1/x) = √3, then find the value of x18 + 1/x18.1). -22). √33). 24). 0

Answer»

⇒ x + 1/x = √3

Squaring both sides we GET,

⇒ x2 + (1/x2) + 2 = 3

⇒ x2 + (1/x2) = 1

Now, CUBING both sides we get,

⇒ x6 + (1/x6) + 3 × x2 × (1/x2){x2 + (1/x2)} = 1

⇒ x6 + (1/x6) + 3(1) = 1

⇒ x6 + (1/x6) = -2

Now, cubing both sides we get,

⇒ x18 + (1/x18) + 3 × x6 × (1/x6){x6 + (1/x6)} = -8

⇒ x18 + (1/x18) + 3(-2) = -8

⇒ x18 + (1/x18) = -2


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