Absolute Value - How to proof?

👨🏻‍🏫 學術台數學

GarlicIsDumAss

2011-03-31 1:12 pm

|x-a| + |x+b| = 10

How do we use value a and b such that the equation has infinite solutions or at least one solution?

更新1:

自由自在: what are these formula all about: (10 -a -b) / 2; (10 +a +b) / 2. Don't jump steps and you've to explain it more precisely. Don't forget to explain the ranges.

回答 (1)

用戶9112

2011-04-01 5:05 am

✔ 最佳答案

http://i1090.photobucket.com/albums/i376/Nelson_Yu/1-180.jpg

圖片參考：http://i1090.photobucket.com/albums/i376/Nelson_Yu/1-180.jpg

2011-04-03 14:04:27 補充：
x=(10+a-b)/2
x - a>=0 => (10+a-b)/2 - a >= 0
(10 + a - b - 2a)/2 >= 0 => 10 >= a + b
x + b >= 0 => (10+a-b)/2 + b >= 0
(10 + a - b + 2b)/2 >= 0 => a + b >= -10, etc

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