4MA1/2H Jun 2023, Question 23: Surds
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 4 marks
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The question, in short
A cuboid has a square cross section with edges x cm and length (2√5 − 3) cm; its volume is (13 + 6√5) cm³. Without a calculator, find x as a + √b, showing working.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Volume: x²(2√5 − 3) = 13 + 6√5, so x² = (13 + 6√5)/(2√5 − 3)
- 2Multiply top and bottom by (2√5 + 3): top = 99 + 44√5, bottom = 20 − 9 = 11
- 3x² = 9 + 4√5
- 4Try x = a + √5: x² = a² + 5 + 2a√5, so 2a = 4 and a = 2
- 5x = 2 + √5
Answer2 + √5
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