Given x + 1/x = 3 To find x₃ + 1/x₃: (x + 1/x)₃ = x₃ + 3(x₂)(1/x) + 3(x)(1/x)₂ + 1/x₃ = x₃ + 3x + 3/x + 1/x₃ = x₃ + 1/x₃ + 3(x + 1/x) (x + 1/x)₃ = x₃ + 1/x₃ + 3(3) 27 = x₃ + 1/x₃ + 9 x₃ + 1/x₃ = 27 - 9 = 1
If x + 1/x = 3, then what is the value of x₃ + 1/x₃?
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Question context
This question is part of 📏 Arithmetic Aptitude within the broader 🧠 Aptitude Mastery subject and appears in the ASF Airports Security Force preparation collection. Reviewing the answer together with nearby questions helps reinforce the underlying concept and identify how it may appear in competitive exams.