用配方法解下列方程.....
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3X^2+9X-2
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中四數學題，用配方法解下列方程......
2008-11-02 8:40 pm
回答 (3)
2008-11-04 1:12 am
3X^2+9X-2 = 3X²+9X-2
3(X²+3X)-2=0 .......抽公因式
3[(X)²+2(X)(3/2)+(3/2)²]-3(3/2)²-2=0...........a²+2ab+b²
3(X+3/2)²-27/4-2=0
3(X+3/2)²-35/4=0
3(X+3/2)²=35/4
(X+3/2)²=35/12
X+3/2=(35/12)^(1/2) 或 X+3/2=-(35/12)^(1/2)
X=0.208 或 X=-3.21 (三位有效數字)
3(X²+3X)-2=0 .......抽公因式
3[(X)²+2(X)(3/2)+(3/2)²]-3(3/2)²-2=0...........a²+2ab+b²
3(X+3/2)²-27/4-2=0
3(X+3/2)²-35/4=0
3(X+3/2)²=35/4
(X+3/2)²=35/12
X+3/2=(35/12)^(1/2) 或 X+3/2=-(35/12)^(1/2)
X=0.208 或 X=-3.21 (三位有效數字)
參考: 會考數學拿c既人~
2008-11-02 11:39 pm
3x^2 9x-2 = 0
3(x^2 3x) = 2
(x^2 3x) = 2/3 將3除2
x^2 3x (3/2)^2-(3/2)^2 = 2/3
(x 3/2)^2 = 2/3 9/4
(x 3/2)^2 = 35/12 通分母
(x 3/2) = + /-√(35/12)
x = [+ /-√(35/12)]-3/2
x= [√(35/12)]-3/2 or x= [-√(35/12)]-3/2
x = 0.21 or x= -3.21
3(x^2 3x) = 2
(x^2 3x) = 2/3 將3除2
x^2 3x (3/2)^2-(3/2)^2 = 2/3
(x 3/2)^2 = 2/3 9/4
(x 3/2)^2 = 35/12 通分母
(x 3/2) = + /-√(35/12)
x = [+ /-√(35/12)]-3/2
x= [√(35/12)]-3/2 or x= [-√(35/12)]-3/2
x = 0.21 or x= -3.21
2008-11-02 8:54 pm
3x^2 + 9x - 2 = 0
3*(x^2 + 3x) - 2 = 0
3*(x^2 + 2*1.5x + 1.5^2 - 2.25) -2 = 0
3*(x^2 + 2*1.5x + 1.5^2) -8.75 = 0
3*(x + 1.5)^2 -8.75 = 0
(x + 1.5)^2 = 35/12
x + 1.5 = +√(35/12) or -√(35/12)
x + 1.5 = +√(105)/6 or -√(105)/6
x = +√(105)/6 - 3/2 or -√(105)/6 - 3/2
x = 0.21 or -3.21
3*(x^2 + 3x) - 2 = 0
3*(x^2 + 2*1.5x + 1.5^2 - 2.25) -2 = 0
3*(x^2 + 2*1.5x + 1.5^2) -8.75 = 0
3*(x + 1.5)^2 -8.75 = 0
(x + 1.5)^2 = 35/12
x + 1.5 = +√(35/12) or -√(35/12)
x + 1.5 = +√(105)/6 or -√(105)/6
x = +√(105)/6 - 3/2 or -√(105)/6 - 3/2
x = 0.21 or -3.21
收錄日期: 2021-04-29 16:13:50
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https://hk.answers.yahoo.com/question/index?qid=20081102000051KK00789