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[問題] Pure math (absolute value) again

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Pure math (absolute value) again

A) l x+1 l + l y -1 l = 5                 I x+1 l = 4y - 4

B)   I x-3 l + l x+ 5 l = 8
   

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引用:
原帖由 elvisle 於 2012-5-4 10:02 PM 發表
A) l x+1 l + l y -1 l = 5                 I x+1 l = 4y - 4

B)   I x-3 l + l x+ 5 l = 8
Assume x and y are real numbers.
A:




B:




[ 本帖最後由 howardc64 於 2012-5-5 07:06 PM 編輯 ]
附件: 您所在的用戶組無法下載或查看附件

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我想問我咁樣做左 係咪D CONCEPT 錯哂

b)
l x-3 l + l x+5 l = 8
l x-3+8-8 l + l x+5 l = 8
l x+5 - 8 l + l x+5 l = 8
l 8 - (x+5) l = 8 - l x+5 l
then
8 - (x+5) = +/- ( 8 - l x+5 l )
3-x = +/- ( 8 - l x+5 l )
after that
3-x = 8 - l x+5 l
l x+5 l = 5+x
x+5 = +/- (5+x )
x= 0,-5
and
3-x = -8 - l x+5 l
x+5 = +/- (11-x)
x=3,0

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引用:
原帖由 elvisle 於 2012-5-5 10:05 AM 發表 我想問我咁樣做左 係咪D CONCEPT 錯哂 b) l x-3 l + l x+5 l = 8l x-3+8-8 l + l x+5 l = 8l x+5 - 8 l + l x+5 l = 8 l 8 - (x+5) l = 8 - l x+5 lthen8 - (x+5) = +/- ( 8 - l x+5 l )3-x ...
Yes, mostly when doing abs question, we will rather do the case classification,
you may find that even if you put the real number within the rage [-5, 3], the answer is still correct

[ 本帖最後由 龍嘯天 於 2012-5-5 11:29 AM 編輯 ]

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O  many thanks

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引用:
原帖由 elvisle 於 2012-5-5 10:05 AM 發表
我想問我咁樣做左 係咪D CONCEPT 錯哂

b)
l x-3 l + l x+5 l = 8
l x-3+8-8 l + l x+5 l = 8
l x+5 - 8 l + l x+5 l = 8
l 8 - (x+5) l = 8 - l x+5 l
then
8 - (x+5) = +/- ( 8 - l x+5 l )
3-x ...
You need to specify the range of x in each case every time when you remove a abs value sign!
Also, |x+5|=x+5 <-- this equation actually implies x>=-5 are solutions, not just 0 and -5 !!
Just think of this equation |k|=k, and here k will be any +ve real number.

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引用:
原帖由 howardc64 於 2012-5-4 11:29 PM 發表


Assume x and y are real numbers.







A:
40187




B:
40186
40186
why l x + 5 l = 5 - x for x</= -5 ???

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引用:
原帖由 elvisle 於 2012-5-5 04:08 PM 發表

why l x + 5 l = 5 - x for x
Recall the definition of abs values,
|x|=-x when x<=0
Therefore,
|x+5|=-(x+5) when x+5<=0
|x+5|=-5-x  when x<=-5

[ 本帖最後由 howardc64 於 2012-5-5 07:06 PM 編輯 ]

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why - (x+5) doesn't equal -x - 5 but 5-x?

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回覆 9# elvisle 的帖子

Oh, I misread it. You are correct.
I have edited my answer in #2.
Sorry for that.

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