4PM1/02 Jun 2023, Question 1: Surds
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 5 marks
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The question, in short
Rationalise the denominator of (a + 2√5)/(3 − √5), equate it to (11 + b√5)/2, and find integer a and prime b, showing working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1(a + 2√5)/(3 − √5) × (3 + √5)/(3 + √5) = (3a + a√5 + 6√5 + 10)/(9 − 5)
- 2= (3a + 10 + (6 + a)√5)/4
- 3Equate with (11 + b√5)/2: (3a + 10)/4 = 11/2, so 3a + 10 = 22, a = 4
- 4(6 + a)/4 = b/2, so b = (6 + 4)/2 = 5
Answera = 4, b = 5
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