一元二次方程式

2006-12-19 10:08 pm
求 x^2 - 11x +16 = 0 的根

回答 (2)

2006-12-19 10:17 pm
✔ 最佳答案
方法一:配方
x² - 11x + 16 = 0
x² - 2(11/2)x + (11/2)² - (11/2)² + 16 = 0
[x - (11/2)]² - 121/4 + 16 = 0
[x - (11/2)]² - 57/4 = 0
[x - (11/2)]² = 57/4
x - (11/2) = ±√(57/4)
x - (11/2) = ±√57/√4
x - (11/2) = ±√57/2
x = ±√57/2 + 11/2
x = √57/2 + 11/2 or x = -√57/2 + 11/2
x = (11+√57)/2 or x = (11-√57)/2
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方法二:公式
x² - 11x + 16 = 0
x = [-(-11)±√[(-11)²-4(1)(16)]/2(1)
x = [11±√57]/2
x = (11±√57)/2
x = (11+√57)/2 or x = (11-√57)/2
2006-12-20 2:02 am
Use formula !!
[11+(11^2-4(1)(16))^0.5]/(2*1) or [11-(11^2-4(1)(16))^0.5]/(2*1)
Ans =1.725 or 9.275
參考: casio super-FX


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