A.Math Absolute value

👨🏻‍🏫 學術台數學

Tom

2007-10-02 12:27 am

28a)
Solve |1-x|=2

b)
By considering the cases x≦1 and x＞1, or otherwise, solve |1-x|=x-1.

我b連應該什樣做也不知道＝　＝，應什樣用 x≦1 and x＞1？

更新1:

But .... the answer is x≧1

更新2:

Actually, I agree with your means to solve this question.May you have a check with your answer? Maybe the answer in the book is wrong.

回答 (2)

toyszchun

2007-10-02 12:40 am

✔ 最佳答案

28a)
|1-x|=2
1-x=2 OR 1-x=-2
x=-1 or 3

b)
consider |1-x|:
If x≦1,|1-x|=1-x (因為x≦1得出1-x≧0)
If x＞1,|1-x|=-(1-x) (因為x＞1得出1-x＜0)

(上面的只是解釋給你看,考試時不用寫的)
Case 1: x≦1
|1-x|=1-x
1-x = 1-x
x=x
∴It is true for all real x when x≦1

Case 2: x＞1
|1-x|=1-x
-(1-x) = 1-x
x-1=1-x
2x=0
x=0 (rejected,因為x＞1)

∴The solution is x≦1

2007-10-01 16:41:52 補充：
最後幾步寫錯了x-1=1-x應該是:2x = 2x = 1(rejected,因為x＞1)但結果都是一樣

2007-10-04 18:58:07 補充：
抱歉,我找不到我錯在哪裡

👍 0 👎 0

day

2007-10-25 10:02 am

條題目係solve |1-x|=x-1...
唔係solve |1-x|=1-x

👍 0 👎 0

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