WMA11/01 Oct 2019, Question 8: Hidden Quadratics
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 5 marks
The question, in short
Solve by algebra the equation x − 6x^(1/2) + 4 = 0, giving answers fully simplified in the form a + b√c with integers a, b, c.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1Let u = x^(½): u² − 6u + 4 = 0
- 2u = (6 ± √(36 − 16))/2 = 3 ± √5
- 3Both values are positive, so both are valid square roots
- 4x = (3 ± √5)² = 9 ± 6√5 + 5
- 5x = 14 + 6√5 or x = 14 − 6√5
Answerx = 14 + 6√5, x = 14 − 6√5
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