F.3升 F.4 Maths 40分急!

1) http://img130.imageshack.us/img130/3576/66643012.jpg
證角ABD=角ACE

2a) (x+2) (x-4) +5
=x^2-2x-8+5
=(x-3)(x+1)
2b) Let y^2-2y=x
(y^2-2y+2)(y^2-2y-4)+5
=(x+2)(x-4)+5 <--- =equation in 2a
=(x-3)(x+1)
=(y^2-2y-3)(y^2-2y+1)
=(y-3)(y+1)(y-1)^2

(1) Find the slope of AB and the slope of BC.
If they are the slope of AB is equal to slope of BC, then points A, B and C are collinear.

slope of AB= (3 - 2)/(-2-0 ) = -1/2
slope of BC = (--1 -2)/(6-0) = -3/6 = -1/2

They are the same, hence A,B and C are collinear

Alternative, find the linear equation- the straight line passing through point A and point B

The y-intercept is +2 from the point b(0, 2)
the slope is -1/2
The Equation is y = -1/3 x + 2

Substitute point C (6, -1) into that equation
-1 = -1/2(6) + 2
-1 = -1
Since they are equal, hence A, B and C are collinear

(2) A:
(x+2) (x-4) +5
Expand
x^2 +2x -4x -8 +5
x^2 -2x - 3
(x-3)(x + 1)

Hence (x+2) (x-4) +5 can be factorized
= (x-3)(x + 1)

2-B
Let x = y^2 - 2y
(y^2-2y+2) (y^2-2y-4)+5 can be rearranged as (x+2) (x-4) +5
Since (x+2) (x-4) +5 = (x-3)(x + 1)
Let (x - 3) (x + 1) = (y^2 - 2y - 3) ( y^2 - 2y + 1)
(y^2-2y+2) (y^2-2y-4)+5 = (y^2 - 2y - 3) ( y^2 - 2y + 1)
= (y-3)(y + 1) (y -1) (y-1)

2010-08-08 01:04:12 補充：
In this sentence,

If they are the slope of AB is equal to slope of BC, then points A, B and C are collinear.

Delete the "they are"

Correction:
If the slope of AB is equal to slope of BC, then points A, B and C are collinear.