4PM1/01R Jun 2024, Question 1: Surds
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 4 marks
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The question, in short
Solve √50 x − √18 > 6x + 5 without a calculator, giving the answer exactly with a rationalised denominator and showing working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 1√50 x − 6x > 5 + √18
- 2x > (5 + √18)/(√50 − 6) (√50 − 6 > 0, so the sign stays)
- 3Multiply top and bottom by (√50 + 6)
- 4(5√50 + 30 + √18√50 + 6√18)/(50 − 36) = (25√2 + 30 + 30 + 18√2)/14
- 5x > (43√2 + 60)/14
Answerx > (43√2 + 60)/14
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