4MA1/2HR Jan 2022, Question 13: Surds
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 3 marks
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The question, in short
Given a = √8 + 4 and b = √8 − 4, use the product (a − b)(a + b), written as y√(4y), to find y, showing working.
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Solution · 3 marks
- 1a − b = (√8 + 4) − (√8 − 4) = 8
- 2a + b = (√8 + 4) + (√8 − 4) = 2√8
- 3(a − b)(a + b) = 8 × 2√8 = 16√8
- 4The required form is y√(4y) = y × 2√y = 2y√y
- 5Matching 2y√y with 16√8 gives 2y = 16 and √y = √8
- 6y = 8
Answer8
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