Simultaneous equations....急!!!

As follows:


圖片參考：http://i707.photobucket.com/albums/ww74/stevieg90/10-34.jpg



圖片參考：http://i707.photobucket.com/albums/ww74/stevieg90/11-29.jpg


2010-09-10 12:37:19 補充：
http://i707.photobucket.com/albums/ww74/stevieg90/10-34.jpg
http://i707.photobucket.com/albums/ww74/stevieg90/11-29.jpg

2010-09-11 16:17:56 補充：
Sorry for some mistakes in Q3 and Q4.
Answer for Q3 should be y=-2 and x=3 (rejected x=-3)
Answer for Q4 should be y=0 and x=c (rejected x=-c)

1) y=2x^2+x+2
y=2x+1
Sol
2x+1=2x^2+x+2
2x^2－x+1=0
(2x+1)(x－1)=0
x=－1/2 or x=1
(a) x=－1/2
y=2x+1=－1+1=0
(b) x=1
y=2x+1=2+1=3

2) x^2 + y^2 = 4
x + y = 6
Sol
y=6-x
x^2+y^2=4
x^2+(6－x)^2=4
2x^2－12x+36=4
x^2－6x+16=0
x=(6+/-√(36-64))/2=3+/-i√7
(a) x=3+i√7，y=3－i√7
(b)x=3－i√7，y=3+i√7

3) x^2－2y^2=3x+4y=1
Sol
3x=1－4y
x^2－2y^2=1
9x^2－18y^2=9
(1－4y)^2－18y^2－9=0
16y^2－8y+1－18y^2－9=0
－2y^2－8y－8=0
y^2+4y+4=0
(y+2)^2=0
y=－2(double roots)
3x=1+8=9
x=3

4) x^2 + y^2 = c^2
x + y = c
Sol
y=c－x
x^2+(c－x)^2=c^2
x^2+x^2－2cx+c^2=c^2
2x^2－2cx=0
x(x－c)=0
x=0 or x=c
(a) x=0 =>y=c
(b) x=c=>y=0

5) A 2-digit number is increased by 45 when the digits are reversed. Theproduct
of the digits is 36. Find the number.
Sol
設此數為xy=10x+y
(10y+x)－(10x+y)=45
9(y－x)=45
y－x=5
y=x+5
xy=36
x(x+5)=36
x^2+5x－36=0
(x－4)(x+9)=0
x=4 or x=－9(不合)
此數=49