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急!!!f4一元二次方程數學
發問:
化簡下列各數式，並以a+bi的形式表示答案。1)5/4-3i2)-8i/3+6i求下列各二方程。3)8x^2+7x=04)(a+1) ^2-4(a-1) ^2=0求下列各二次方程的根。5)(2y+3)(2y-3)=5y6) 解36(x-1) ^2-25=0利用平方根解二次方程7)36(x+2) ^2-7=0解下列二次方程8)x ^2+(x-3) ^2=4設a和b為二次方程15x^2+11x-12=0的根，其中a
最佳解答:
1) 5 / (4 - 3i) = 5(4 + 3i) / (4 - 3i)(4 + 3i) = 5(4 + 3i) / (42 + 32) = 5(4 + 3i) / 25 = (4 + 3i) / 5 2) -8i / (3 + 6i) = -8i(3 - 6i) / (3 + 6i)(3 - 6i) = (-48 - 24i) / (32 + 62) = (-48 - 24i) / 45 = (-16 - 8i) / 15 3) 8x2 + 7x = 0 x(8x + 7) = 0 x = 0 或 8x + 7 = 0 x = 0 或 x = -7/8 4) (a + 1)2 - 4(a - 1)2 = 0 (a + 1)2 - [2(a - 1)]2 = 0 (a + 1)2 - (2a - 2)2 = 0 [(a + 1) + (2a - 2)] [(a + 1) - (2a - 2)] = 0 (a + 1 + 2a - 2)(a + 1 - 2a + 2) = 0 (3a - 1)(-a + 3) = 0 3a - 1 = 0 或 -a + 3 = 0 a = 1/3 或 a = 3 5) (2y + 3)(2y - 3) = 5y (2y)2 - 32 = 5y 4y2 - 5y - 9 = 0 (4y - 9)(y + 1) = 0 4y - 9 = 0 或 y + 1 = 0 y = 9/4 或 y = -1 6) 36(x - 1)2 - 25 = 0 36(x - 1)2 = 25 (x - 1)2 = 25/36 x - 1 = 5/6 或 x - 1 = -5/6 x = 11/6 或 x = 1/6 7) 36(x + 2)2 - 7 = 0 36(x + 2)2 = 7 (x + 2)2 = 7/36 x + 2 = (√7)/6 或 x + 2 = -(√7)/6 x = (-12 + √7)/6 或 x = (-12 -√7)/6 8) x2 + (x - 3)2 = 4 x2 + x2 - 6x + 9 = 4 2x2 - 6x + 5 = 0 x = [6 + √(62 - 4*2*5)] / (2 * 2) 或x = [6 - √(62 - 4*2*5)] / (2 * 2) x = (6 + 2i)/4 或 x = (6 - 2i)/4 x = (3 + i)/2 或 x = (3 - i)/2 9. a 和 b 為二次方程 15x2 + 11x - 12 = 0 的根 兩根之和： a + b = -11/15 兩根之積： ab = -12/15 設所求方程為： x2 + px + q = 0 p = -[(1/a) + (1/b)] = - (a + b)/ab = - (-11/15) / (-12/15) = -11/12 q = (1/a) x (1/b) = 1 / ab = 1 / (-12/15) = -15/12 所求的方程： x2 - (11/12)x - (15/12) = 0 12x2 - 11x - 15 = 0
如果你要交功課，還是自己用心去想。過程很重要呀。
急!!!f4一元二次方程數學
發問:
化簡下列各數式，並以a+bi的形式表示答案。1)5/4-3i2)-8i/3+6i求下列各二方程。3)8x^2+7x=04)(a+1) ^2-4(a-1) ^2=0求下列各二次方程的根。5)(2y+3)(2y-3)=5y6) 解36(x-1) ^2-25=0利用平方根解二次方程7)36(x+2) ^2-7=0解下列二次方程8)x ^2+(x-3) ^2=4設a和b為二次方程15x^2+11x-12=0的根，其中a
最佳解答:
1) 5 / (4 - 3i) = 5(4 + 3i) / (4 - 3i)(4 + 3i) = 5(4 + 3i) / (42 + 32) = 5(4 + 3i) / 25 = (4 + 3i) / 5 2) -8i / (3 + 6i) = -8i(3 - 6i) / (3 + 6i)(3 - 6i) = (-48 - 24i) / (32 + 62) = (-48 - 24i) / 45 = (-16 - 8i) / 15 3) 8x2 + 7x = 0 x(8x + 7) = 0 x = 0 或 8x + 7 = 0 x = 0 或 x = -7/8 4) (a + 1)2 - 4(a - 1)2 = 0 (a + 1)2 - [2(a - 1)]2 = 0 (a + 1)2 - (2a - 2)2 = 0 [(a + 1) + (2a - 2)] [(a + 1) - (2a - 2)] = 0 (a + 1 + 2a - 2)(a + 1 - 2a + 2) = 0 (3a - 1)(-a + 3) = 0 3a - 1 = 0 或 -a + 3 = 0 a = 1/3 或 a = 3 5) (2y + 3)(2y - 3) = 5y (2y)2 - 32 = 5y 4y2 - 5y - 9 = 0 (4y - 9)(y + 1) = 0 4y - 9 = 0 或 y + 1 = 0 y = 9/4 或 y = -1 6) 36(x - 1)2 - 25 = 0 36(x - 1)2 = 25 (x - 1)2 = 25/36 x - 1 = 5/6 或 x - 1 = -5/6 x = 11/6 或 x = 1/6 7) 36(x + 2)2 - 7 = 0 36(x + 2)2 = 7 (x + 2)2 = 7/36 x + 2 = (√7)/6 或 x + 2 = -(√7)/6 x = (-12 + √7)/6 或 x = (-12 -√7)/6 8) x2 + (x - 3)2 = 4 x2 + x2 - 6x + 9 = 4 2x2 - 6x + 5 = 0 x = [6 + √(62 - 4*2*5)] / (2 * 2) 或x = [6 - √(62 - 4*2*5)] / (2 * 2) x = (6 + 2i)/4 或 x = (6 - 2i)/4 x = (3 + i)/2 或 x = (3 - i)/2 9. a 和 b 為二次方程 15x2 + 11x - 12 = 0 的根 兩根之和： a + b = -11/15 兩根之積： ab = -12/15 設所求方程為： x2 + px + q = 0 p = -[(1/a) + (1/b)] = - (a + b)/ab = - (-11/15) / (-12/15) = -11/12 q = (1/a) x (1/b) = 1 / ab = 1 / (-12/15) = -15/12 所求的方程： x2 - (11/12)x - (15/12) = 0 12x2 - 11x - 15 = 0
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其他解答:如果你要交功課，還是自己用心去想。過程很重要呀。
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