4PM1/02 Jun 2025, Question 3: Surds
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 5 marks
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The question, in short
Given (a + b√5)/(6 − 2√5) = (9 + 4√5)/c with a, b, c prime, find the values of a, b and c.
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Solution · 5 marks
- 1Multiply top and bottom by (6 + 2√5): denominator 36 − 20 = 16
- 2Numerator (6a + 10b) + (2a + 6b)√5
- 3So [(3a + 5b) + (a + 3b)√5]/8 = (9 + 4√5)/c
- 4With c = 8: 3a + 5b = 9, a + 3b = 4, giving a = 7/4, b = 3/4
- 5Multiply by 4: (7 + 3√5)/(6 − 2√5) = (9 + 4√5)/2, so a = 7, b = 3, c = 2
Answera = 7, b = 3, c = 2
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