Question
If x + 1/x = 3 (x ≠ 0), find the value of x³ + 1/x³.
Solution
(x + 1/x)² = x² + 1/x² + 2 = 3² = 9 ⇒ x² + 1/x² = 9 − 2 = 7 Now use identity: x³ + 1/x³ = (x + 1/x)(x² + 1/x² − 1) = 3 × (7 − 1) = 3 × 6 = 18.
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