FOUR 四 4 條MATHS

x^3-3x^2-4x+12
=(x+2)(x^2-5x+6)
=(x+2)(x-2)(x-3)

f(-0.5)=0
(-0.5)^3+a(-0.5)^2+3(-0.5)=0
-0.125+0.25a-1.5=0
0.25a=1.625
a=6.5

3)Let x and y the the two numbers and x>y.
Then x^2+y^2=17 and
(x-y)^2=9
x^2-2xy+y^2=9
(x^2+y^2)-2xy=9
17-2xy=9
2xy=8
xy=4
(x,y)=(4,1) or (x,y)=(2,2)(Rejected)

4a)x^2+y^2=34^2 (Pyth. Theorem)
x^2+y^2=1156
4b)xy/2=240
xy=480
4c)(x^2+y^2)+2xy=1156+2(480)
(x+y)^2=1716
x+y=46
(x^2+y^2)-2xy=1156-2(480)
(x-y)^2=196
x-y=14
We have x+y=46 and x-y=14.
(x+y)+(x-y)=46+14
2x=50
x=25
(x+y)-(x-y)=46-14
2y=32
y=16
(x,y)=(25,16)

2008-06-02 17:06:23 補充：
更正內容：
(x+y)+(x-y)=46+14
2x=60
x=30
(x+y)-(x-y)=46-14
2y=32
y=16
(x,y)=(30,16)