4PM1/01 Jun 2022, Question 1: Surds
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 3 marks
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The question, in short
Rationalise the fraction (2√3 − 4)/(3√3 + 5) and express it as a + b√3, finding the integer values of a and b without a calculator.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1Multiply top and bottom by 3√3 − 5
- 2Numerator: (2√3 − 4)(3√3 − 5) = 18 − 10√3 − 12√3 + 20 = 38 − 22√3
- 3Denominator: (3√3)² − 5² = 27 − 25 = 2
- 4(38 − 22√3)/2 = 19 − 11√3, so a = 19, b = −11
Answera = 19, b = −11 (19 − 11√3)
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