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0606/12 May/Jun 2025, Question 2: Hidden Quadratics and Harder Simultaneous Equations

Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Solve the equation x^(1/3) + 1 = 6/x^(1/3) for x.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Solution · 4 marks

  1. 1Multiply through by x^(1/3): x^(2/3) + x^(1/3) − 6 = 0
  2. 2(x^(1/3) + 3)(x^(1/3) − 2) = 0
  3. 3x^(1/3) = −3 or x^(1/3) = 2
  4. 4x = −27 or x = 8

Answerx = −27, x = 8

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Also searched as: 0606/12/M/J/25 · 0606_s25_qp_12 · 0606 s25 12 · question 2.
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