4PM1/02 Jan 2023, Question 2: The Cosine Rule
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 4 marks
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The question, in short
Using the triangle with sides x + 2, 2x + 4 and 2x − 1 and a 60° angle, determine x and express it as p + q√3 with integers p and q.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Cosine rule: (2x − 1)² = (2x + 4)² + (x + 2)² − 2(2x + 4)(x + 2) cos 60°
- 24x² − 4x + 1 = 4x² + 16x + 16 + x² + 4x + 4 − (2x² + 8x + 8)
- 3x² − 16x − 11 = 0
- 4x = (16 ± √(256 + 44))/2 = 8 ± 5√3
- 58 − 5√3 makes 2x − 1 negative, so x = 8 + 5√3
Answerx = 8 + 5√3
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