4PM1/01 Nov 2023, Question 1: Surds
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 4 marks
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The question, in short
Given a right-angled triangle with AB = (2 + 4√5) cm and area (34 + 11√5) cm², find integers a and b in BC = (a + b√5) cm without a calculator.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1(1/2)(2 + 4√5)(a + b√5) = 34 + 11√5
- 2a + b√5 = (34 + 11√5)/(1 + 2√5)
- 3Multiply by (1 − 2√5)/(1 − 2√5): (34 − 68√5 + 11√5 − 110)/(1 − 20)
- 4= (−76 − 57√5)/(−19) = 4 + 3√5
- 5a = 4, b = 3
Answera = 4, b = 3
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