A maths問題

1. Case 1: x<=-4
-(2x-1) - (x+4) = 9
-2x+1-x-4 = 9
-3x = 12
x = -4 ...(1)
Case 2: -4<x<1/2
-(2x-1) +x+4 = 9
-2x+1+x+4 = 9
-x = 4
x = -4 (rejected)
Case 3: x>=1/2
2x-1+x+4 = 9
3x + 3 = 9
x = 2 ...(2)
Combining (1) and (2), x = -4 or 2
2. |x-2|(x-3)=2
Case 1: x >=2
(x-2)(x-3) = 2
x^2 - 5x +6 = 2
x^2 - 5x + 4 = 0
(x-4)(x-1) = 0
x = 4 or 1 (rejected)
x = 4
Case 2: x < 2
-(x-2)(x-3) = 2
-x^2 +5x-6 = 2
x^2 - 5x +8 = 0
No solution
Hence x = 4

1.
2x-1+x+4=9
3x+3=9
3(x+1)=9
3(x+1)/3=9/3
x+1=3
x+1-1=3-1
x=2

p.s. step2
如果先減3的話,會複雜一些,容易出錯



2.
x-2(x-3)=2
x-2x+6=2
(-x)+6-6=2-6
(-x)=(-4)
x=4

p.s.
最後的答案不能為 (-x)=(-4) 要刪去負號

2007-11-22 23:59:23 補充：
如果 | 是括號的話,第2題便做不到了

1.[2x-1|+|x+4|=9 睇下個付號~係+就拆括號~*就分解
2x-1+x+4=9
3x=6
x=2

2. x-2|(x-3)=2 x*x=x既2次
x*x-5x+6 =2
x*x-5x+[5/2]*[5/2]-[5/2]*[5/2]+6=2 [5/2]*[5/2]=[5/2]既2次
[x-[5/2]]*[x-[5/2]]-[5/2]*[5/2]+6 =2
[x-[5/2]]*[x-[5/2]] = 1/4
x-[5/2] = 1/2
x = 3 其實答案有2個 ~通常d人都係用呢個

1). (2x-1)+(x+4)=9
2x-1+x+4 =9
3x+3 =9
3x =6
x =2