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    Question

    If x ≠ 0 and x − 1/x = 5, find: (i) x² +

    1/x² (ii) x³ − 1/x³
    A 27 and 140 Correct Answer Incorrect Answer
    B 32 and 200 Correct Answer Incorrect Answer
    C 33 and 165 Correct Answer Incorrect Answer
    D 45 and 182 Correct Answer Incorrect Answer

    Solution

    ATQ, Given: x − 1/x = 5 (i) Square both sides: (x − 1/x)² = 25 x² + 1/x² − 2 = 25 ⇒ x² + 1/x² = 27 (ii) Cube both sides using identity: (x − 1/x)³ = x³ − 1/x³ − 3(x − 1/x) So: 5³ = x³ − 1/x³ − 3·5 125 = x³ − 1/x³ − 15 ⇒ x³ − 1/x³ = 125 + 15 = 140

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