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0606/22 Feb/Mar 2025, Question 3: Hidden Quadratics and Harder Simultaneous Equations

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 4 marks

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The question, in short

Solve 6x^(3/5) + 1 = 12/x^(3/5) and give the answers correct to 2 decimal places.

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Solution · 4 marks

  1. 1Multiply by x^(3/5): 6x^(6/5) + x^(3/5) − 12 = 0
  2. 2Let u = x^(3/5): 6u² + u − 12 = 0
  3. 3(3u − 4)(2u + 3) = 0, so u = 4/3 or u = −3/2
  4. 4x = (4/3)^(5/3) = 1.62
  5. 5x = (−3/2)^(5/3) = −1.97

Answerx = 1.62, x = −1.97

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