4PM1/01R Jan 2020, Question 1: Surds
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 4 marks
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The question, in short
Rationalise the fraction (a + √3)/(2 − √3), equate it to 11 + b√3, and find the integer values of a and b.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1Multiply top and bottom by (2 + √3): denominator (2 − √3)(2 + √3) = 1
- 2(a + √3)(2 + √3) = 2a + a√3 + 2√3 + 3 = (2a + 3) + (a + 2)√3
- 3Compare with 11 + b√3: 2a + 3 = 11 and b = a + 2
- 4a = 4, b = 6
Answera = 4, b = 6
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