中四聯立方程問題

冰龍仔仔

1:
x-y-1=0
x^2-xy+y^2=7
2:
x-4y-6=0
x^2+2xy-36=0
3:
y=2x^2-3x+k
y=5x-7
唔該晒

AYuMe

1.x - y - 1=0
x = y + 1 ... (1
x^2 - xy + y^2 = 7 ... (2

代(1 入(2 ,
(y + 1)^2 - (y + 1)y + y^2 = 7
y^2 + y - 6 = 0
(y - 3)(y + 2) = 0
y = 3 或 y = -2
x = 4 或 x = -1

2.x - 4y - 6 = 0
x = 4y + 6 ... (1
x^2 + 2xy - 36 = 0 ... (2

代(1 入(2 ,
(4y + 6)^2 + 2(4y + 6)y - 36 = 0
8y^2 + 36y = 0
2y^2 + 9y = 0
y(2y + 9) = 0
y = 0 或 y = -9/2
x = 6 或 y = -12

3.y = 2x^2 - 3x + k ... (1
y = 5x - 7 ... (2
代(1 入(2 ,
2x^2 - 3x + k = 5x - 7
2x^2 - 8x + (7 + k) = 0

第三題兩條公式 , 有三個未知數 應該係計唔到
除非有其他條件

[ 本帖最後由 AYuMe 於 2009-4-15 09:56 PM 編輯 ]

Sikkwong

第三條如果加返個(x有等根)就做到
y=2x^2-3x+k ----(1)
y=5x-7  ----(2)
代(2)入(1),可得
2x^2-3x+k=5x-7
2x^2- 8x+ k+7=0<----(3)
利用(b^2-4ac)
(-8)^2-4(2)(k+7)=0
64-8k-56=0
k=1
代k=1入(3)
2x^2- 8x+ 8=0
X=2
代x=2入(2)
y=5(2)-7
y=3

請不要為我傷心

代(1 入(2 ,
(y + 1)^2 - (y + 1)y + y^2 = 7
y^2 + y - 6 = 0
(y - 3)(y + 2) = 0
y = 3 或 y = -2
x = 4 或 x = -1

好似計錯.. 應該係  y = -3.. 2 wo...