Simplification · Question 30 · Hard
If x = 1/(2 − √3), find the value of x³ − 2x² − 7x + 5.
- 5
- 3
- 2√3
- 1
Answer and explanation
Answer: B. 3
Explanation: x = 2 + √3, so x² − 4x + 1 = 0, i.e. x² = 4x − 1 and x³ = 4x² − x = 15x − 4. Then x³ − 2x² − 7x + 5 = (15x − 4) − (8x − 2) − 7x + 5 = 3.
Previous: Find the value of √(10 + √(25 + √(108 + √(154 + √225)))).
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