4MA1/1H Jun 2024, Question 17: Surds
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 3 marks
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The question, in short
Rationalise the denominator of (1 + √5)/(3 − √5) and show it equals a + √b with a and b integers, showing all steps.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1Multiply the top and the bottom by 3 + √5
- 2Bottom: (3 − √5)(3 + √5) = 9 − 5 = 4
- 3Top: (1 + √5)(3 + √5) = 3 + √5 + 3√5 + 5 = 8 + 4√5
- 4So the fraction is (8 + 4√5)/4
- 5Divide each part by 4: 2 + √5
- 6So the expression is 2 + √5, as required
Answer2 + √5
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