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標題:
maths(解方程 二 : 代數方法)
發問:
p.230 18. (1/2x+1)[(1/2x+1)+3]=10 27.{ 9x^2 + 2 = 9xy +6y^2 { 3x + 2y = 2 29. y - x^2 +3x = 3x- 2y -4 = 1
最佳解答:
(18) 代 u = 1/2x+1: u(u + 3) = 10 u2 + 3u - 10 = 0 (u - 2)(u + 5) = 0 u = 2 或 - 5 1/2x + 1 = 2 或 - 5 x = 1/2 或 -1/12 (27) 9x2 + 2 = 9xy + 6y2 9x2 + 2 = 3y(3x + 2y) 9x2 + 2 = 3y(2) 9x2 + 2 = 3(2y) 9x2 + 2 = 3(2 - 3x) 9x2 + 9x - 4 = 0 (3x + 4)(3x - 1) = 0 x = -4/3 或 1/3 y = 3 或 1/2 (29) y - x2 + 3x = 1 y = x2 - 3x + 1 ... (1) 3x - 2y - 4 = 1 3x - 2(x2 - 3x + 1) - 3 = 0 - 2x2 + 9x - 7 = 0 2x2 - 9x + 7 = 0 (2x - 7)(x - 1) = 0 x = 7/2 或 1 y = 11/4 或 -1
18.(看不出x是分子或是分母,以下的是以x為分母) (1/2x+1)[(1/2x+1)+3]=10 (1/2x+1)(1/2x+4)=10 1/4x^2+4/2x+1/2x+4=10 1+8x+2x+16x^2=40x^2 <---[同時左右方乘4x^2] 24x^2-10x-1=0 (2x-1)(12x+1)=0 所以x=1/2或x=-1/12 ========================================= 27. 9x^2 + 2 = 9xy +6y^2 ---(1) 3x + 2y = 2 ---(2) 由(2)可得, x=(2-2y)/3---(3) 把(3)代入(1), 9[(2-2y)/3]^2+2=9y[(2-2y)/3]+6y^2 4y^2-8y+4+2=3y(2-2y)+6y^2 2y^2+8y+6y-6y^2-6=0 4y^2-14y+6=0 2y^2-7y+6=0 (2y-1)(y-3)=0 所以y=1/2或y=3 把y=1/2代入(3) x=1/3 把y=3代入(3) x=-4/3 所以解為x=-4/3,y=3或x=1/3,y=1/2 ========================================== 29. y - x^2 +3x = 3x- 2y -4 = 1可分為 ======================== y - x^2 +3x = 3x- 2y -4 x^2-4-3y=0 ---(1) 3x- 2y -4 = 1---(2) 由(2)可得, y=(3x-5)/2 ---(3) 把(3)代入(1) x^2-4-3[(3x-5)/2]=0 2x^2-8-9x+15=0 2x^2-9x+7=0 (2x-7)(x-1)=0 所以x=7/2或x=1 ================ 把x=7/2代入(3) y=11/4 把x=1代入(3) y=-1 所以解為x=7/2,y=11/4或x=1,y=-1 ================ 如有錯誤請指點
maths(解方程 二 : 代數方法)
發問:
p.230 18. (1/2x+1)[(1/2x+1)+3]=10 27.{ 9x^2 + 2 = 9xy +6y^2 { 3x + 2y = 2 29. y - x^2 +3x = 3x- 2y -4 = 1
最佳解答:
(18) 代 u = 1/2x+1: u(u + 3) = 10 u2 + 3u - 10 = 0 (u - 2)(u + 5) = 0 u = 2 或 - 5 1/2x + 1 = 2 或 - 5 x = 1/2 或 -1/12 (27) 9x2 + 2 = 9xy + 6y2 9x2 + 2 = 3y(3x + 2y) 9x2 + 2 = 3y(2) 9x2 + 2 = 3(2y) 9x2 + 2 = 3(2 - 3x) 9x2 + 9x - 4 = 0 (3x + 4)(3x - 1) = 0 x = -4/3 或 1/3 y = 3 或 1/2 (29) y - x2 + 3x = 1 y = x2 - 3x + 1 ... (1) 3x - 2y - 4 = 1 3x - 2(x2 - 3x + 1) - 3 = 0 - 2x2 + 9x - 7 = 0 2x2 - 9x + 7 = 0 (2x - 7)(x - 1) = 0 x = 7/2 或 1 y = 11/4 或 -1
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其他解答:18.(看不出x是分子或是分母,以下的是以x為分母) (1/2x+1)[(1/2x+1)+3]=10 (1/2x+1)(1/2x+4)=10 1/4x^2+4/2x+1/2x+4=10 1+8x+2x+16x^2=40x^2 <---[同時左右方乘4x^2] 24x^2-10x-1=0 (2x-1)(12x+1)=0 所以x=1/2或x=-1/12 ========================================= 27. 9x^2 + 2 = 9xy +6y^2 ---(1) 3x + 2y = 2 ---(2) 由(2)可得, x=(2-2y)/3---(3) 把(3)代入(1), 9[(2-2y)/3]^2+2=9y[(2-2y)/3]+6y^2 4y^2-8y+4+2=3y(2-2y)+6y^2 2y^2+8y+6y-6y^2-6=0 4y^2-14y+6=0 2y^2-7y+6=0 (2y-1)(y-3)=0 所以y=1/2或y=3 把y=1/2代入(3) x=1/3 把y=3代入(3) x=-4/3 所以解為x=-4/3,y=3或x=1/3,y=1/2 ========================================== 29. y - x^2 +3x = 3x- 2y -4 = 1可分為 ======================== y - x^2 +3x = 3x- 2y -4 x^2-4-3y=0 ---(1) 3x- 2y -4 = 1---(2) 由(2)可得, y=(3x-5)/2 ---(3) 把(3)代入(1) x^2-4-3[(3x-5)/2]=0 2x^2-8-9x+15=0 2x^2-9x+7=0 (2x-7)(x-1)=0 所以x=7/2或x=1 ================ 把x=7/2代入(3) y=11/4 把x=1代入(3) y=-1 所以解為x=7/2,y=11/4或x=1,y=-1 ================ 如有錯誤請指點
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