中五數學~請教!

1.) 2x^2 - kx = 48 ... (1)
x + k =18 ... (2)
(2) => k = 18 - x
Sub into(1) => 2x^2 - (18 - x)x = 48
2x^2 - 18x + x^2 = 48
3x^2 - 18x - 48 = 0
x^2 - 6x - 16 = 0
(x - 8)(x + 2) = 0
x = 8 或 x = -2
2.) 設長度 = x cm
闊度 = (x - 4)/2
面積 = x(x - 4)/2 = 70
x^2 - 4x = 140
x^2 - 4x - 140 = 0
(x - 14)(x + 10) = 0
x = 14 或 x = -10 (不合)
它的長度 = 14 cm
3.) 2x + y = 4 ... (1)
y = 3x^2 + 1 ... (2)
(1) => y = 4 - 2x
代入 (2) => 4 - 2x = 3x^2 + 1
3x^2 + 2x - 3 = 0
判別式 = 4 - (4)(3)(-3) = 40 > 0
聯立方程有兩個解。
4.) y = 4x ... (1)
y = kx^2 + 1 ... (2)
代(1)入(2) => 4x = kx^2 + 1
kx^2 - 4x + 1 = 0 只有一個解
判別式 16 - 4k = 0
k = 4
5.) x^2 - x + 1 = k ... (1)
x + 1 = 65/k ... (2)
(1)*(2) => (x + 1)(x^2 - x + 1) = 65
x^3 + 1 = 65
x^3 = 64
x = 4
6.) 設個位數為U,十位數為T
U + T = 9 ... (1)
2U - T^2 = 3 ... (2)
(1) => U = 9 - T
代入(2) => 18 - 2T - T^2 = 3
T^2 + 2T - 15 = 0
(T + 5)(T - 3) = 0
T = 3 或T = -5(不合)
代入(1), U + 3 = 9 => U = 6
這個數是36
7.) 4x^2 - 9y^2 + 5 = 0 ... (1)
2x - 3y = - 10 ... (2)
(1) => 4x^2 - 9y^ = -5
(2x - 3y)(2x + 3y) = -5 ... (3)
(3)/(2) => 2x + 3y = 1/2
x + 3y/2 = 1/4
- x - 3y/2 = - 1/4