急!!幾題absolute value既數幫幫手=]

Roger

2009-03-27 1:19 am

如題,以下都係將absolute value脫除左去,可以有多過一個=]唔該晒呀=]

1) | π-3|
2) | y-3 |;if y<3
3) | 2k-8 |;if k<4
4) | 3r-15 |:if r>5
5) | x-y |;if x<y
6) | x-y |;x>y
7) | x^2 +4 |
8) | 3^2k +5 |:where k is an integer
9) | (a-b)(b-c)(c-a) |:where a,b and c are some real numbers

=]
希望各位能夠幫到我啦=]唔該呀=]盡可能有式就盡寫啦=]唔該啦=]

更新1:

答案可以多過一個-.- 幫下我啦!!!唔該啦!!!!

回答 (1)

用戶2053

2009-03-27 8:12 pm

✔ 最佳答案

1) | π-3|
= π-3 (π= 3.14.....>3)
2) | y-3 |;if y<3
= y-3
3) | 2k-8 |;if k<4
= - (2k - 8) = 8 - 2k
4) | 3r-15 |:if r>5
= 3r-15
5) | x-y |;if x<y
= - (x-y) = y-x
6) | x-y |;x>y
= x-y
7) | x^2 +4 |
= x^2 + 4 (x^2 is '+' )
8) | 3^2k +5 |:where k is an integer
= 3^2k + 5 (3^2k is '+')
9) | (a-b)(b-c)(c-a) |:where a,b and c are some real numbers
當 a>=b>=c , b>=c>=a , c>=a>=b :
|(a-b)(b-c)(c-a)| , |(b-c)(c-a)(a-b)| , |(c-a)(a-b)(b-c)| is (+)(+)(-) = (-) or 0
= - (a-b)(b-c)(c-a)
當 a>=c>=b , b>=a>=c , c>=b>=a :
|(a-b)(b-c)(c-a)| , |(b-c)(c-a)(a-b)| , |(c-a)(a-b)(b-c)| is (+)(-)(-) = (+) or 0
= (a-b)(b-c)(c-a)

圖片參考：http://l.yimg.com/f/i/tw/ugc/rte/smiley_32.gif

2009-03-27 15:29:09 補充：
Corrections of no.2 :

2) | y-3 |;if y<3

= - (y-3) = 3 - y

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