Question
If x + 1/x = 4, find x⁵ + 1/x⁵.
Solution
ATQ,
x² + 1/x² = (4)² − 2 = 14 x³ + 1/x³ = (x + 1/x)(x² + 1/x² − 1) = 4(14 − 1) = 52 x⁴ + 1/x⁴ = (x² + 1/x²)² − 2 = 194 x⁵ + 1/x⁵ = (x + 1/x)(x⁴ + 1/x⁴ − x² − 1/x²) = 4(194 − 14) = 720
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