4MA1/1H Jan 2021, Question 18: Surds
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 3 marks
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The question, in short
Expand (8 − √x)(5 + √x), equate to y√x + 21 with x prime and y integer, then find x and y, showing all working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1(8 − √x)(5 + √x) = 40 + 8√x − 5√x − (√x)²
- 2= 40 + 3√x − x
- 3So 40 + 3√x − x = y√x + 21
- 4Comparing the √x terms gives y = 3
- 5Comparing the number terms gives 40 − x = 21, so x = 19
- 6x = 19, which is prime, and y = 3
Answerx = 19, y = 3
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