x = 1 - ∛2 + ∛4. x⁴ - 3x³ + 9x² - 10x + 1 = _________.?
回答 (1)
2016-03-11 1:55 am
✔ 最佳答案
x = 1 - ∛2 + ∛4x(1 + ∛2 ) = (1 + ∛2)(1 - ∛2 + ∛4)
x(1 + ∛2 ) = (∛1)³ + (∛2)³
x(1 + ∛2 ) = 3
∛2 = 3/x - 1
2 = 27/x³ - 27/x² + 9/x - 1
3x³ = 27 - 27x + 9x²
x³ - 3x² + 9x - 9 = 0
x⁴- 3x³ + 9x² - 9x = 0
x⁴- 3x³ + 9x² - 10x + 1 = - x + 1
x⁴- 3x³ + 9x² - 10x + 1 = - (1 - ∛2 + ∛4) + 1
x⁴- 3x³ + 9x² - 10x + 1 = ∛2 - ∛4
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