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    Question

    If (x² + 1)/x = 3, what is the value of (x¹² + 1)/x

    ⁶ ?
    A 322 Correct Answer Incorrect Answer
    B 488 Correct Answer Incorrect Answer
    C 702 Correct Answer Incorrect Answer
    D None of these Correct Answer Incorrect Answer

    Solution

    Given, (x² + 1)/x = 3 ⇒ (x + 1/x) = 3 ⇒ (x + 1/x)² = 3²   [Squaring on both sides] ⇒ x² + 1/x² + 2 = 9 ⇒ x² + 1/x² = 7 ⇒ (x² + 1/x²)³ = 7³   [Cubing on both sides] ⇒ (x²)³ + (1/x²)³ + 3 .x² . 1/x² (x² + 1/x²) = 343 ⇒ x ⁶ + 1/x ⁶ + 3 (x² + 1/x²) = 343 ⇒ x ⁶ + 1/x ⁶ + 3 * 7 = 343 ⇒ x ⁶ + 1/x ⁶ = 322 ⇒ (x¹² + 1)/x ⁶ = 322

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