Question
If x – 1/x = 9, then x3 –
1/x3 is:Solution
Since, x – 1/x = 15 Cubing both sides we get; x3 – 1/x3 – 3 × (x) × (1/x) × (x – 1/x) = 729 Or x3 – 1/ x3 = 1331 + 3 × 9 = 729 + 27 = 756 Alternate method: If it is given, x – 1/x = n and we have to find x3 – 1/x3, can directly use n3 + 3n. x – 1/x = 9 By using n3 + 3n, where n = 9 => 93 + 3 × 9 => 729 + 27 = 756
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