Question
If x ≠0 and x − 1/x = 5, find: (i) x² +
1/x² (ii) x³ − 1/x³Solution
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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