4MA1/1HR Jan 2023, Question 18: Surds
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks
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The question, in short
Solve the equation √3(x − 2√3) = x + 2√3 and express the answer as a + b√3 with integers a and b, showing working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1Expand the bracket: √3 × x − √3 × 2√3 = x + 2√3, so √3x − 6 = x + 2√3
- 2Collect the x terms: √3x − x = 6 + 2√3, so x(√3 − 1) = 6 + 2√3
- 3x = (6 + 2√3)/(√3 − 1)
- 4Multiply top and bottom by √3 + 1
- 5Bottom: (√3 − 1)(√3 + 1) = 3 − 1 = 2
- 6Top: (6 + 2√3)(√3 + 1) = 6√3 + 6 + 6 + 2√3 = 12 + 8√3
- 7x = (12 + 8√3)/2 = 6 + 4√3
Answer6 + 4√3
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