4PM1/01R Jun 2023, Question 1: Surds
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 4 marks
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The question, in short
Rectangle ABCD has sides (4 − √2) cm and (a + b√2) cm, with area (10 + √2) cm². Find the integer values of a and b, showing working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1(4 − √2)(a + b√2) = 10 + √2
- 2a + b√2 = (10 + √2)/(4 − √2)
- 3= (10 + √2)(4 + √2)/((4 − √2)(4 + √2)) = (42 + 14√2)/14
- 4= 3 + √2, so a = 3, b = 1
Answera = 3, b = 1
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