更新1:
I believe one of them is 3. Can't figure out the other.
What are the two solutions of the equation |x-1|+|x-2|=3?
回答 (2)
2015-09-11 5:52 am
x = 0 & 3..by inspection
2015-09-11 6:06 am
|x - 1| + |x - 2| = 3
Case 1 : When x < 1 (|x - 1| = -(x - 1) and |x - 2| = -(x - 2))
|x - 1| + |x - 2| = 3
-(x - 1) - (x - 2) = 3
x = 0
Case 2 : When 1 ≤ x < 2 (|x - 1| = x - 1 and |x - 2| = -(x - 2))
|x - 1| + |x - 2| = 3
(x - 1) - (x - 2) = 3
1 = 3
There is no solution in Case 2.
Case 3 : When x ≥ 2 (|x - 1| = x - 1 and |x - 2| = x - 2)
|x - 1| + |x - 2| = 3
(x - 1) + (x - 2) = 3
2x - 3 = 3
x = 3
Hence, x = 0 or x = 3 ...... (Ans)
Case 1 : When x < 1 (|x - 1| = -(x - 1) and |x - 2| = -(x - 2))
|x - 1| + |x - 2| = 3
-(x - 1) - (x - 2) = 3
x = 0
Case 2 : When 1 ≤ x < 2 (|x - 1| = x - 1 and |x - 2| = -(x - 2))
|x - 1| + |x - 2| = 3
(x - 1) - (x - 2) = 3
1 = 3
There is no solution in Case 2.
Case 3 : When x ≥ 2 (|x - 1| = x - 1 and |x - 2| = x - 2)
|x - 1| + |x - 2| = 3
(x - 1) + (x - 2) = 3
2x - 3 = 3
x = 3
Hence, x = 0 or x = 3 ...... (Ans)
收錄日期: 2021-04-18 00:12:04
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https://hk.answers.yahoo.com/question/index?qid=20150910214326AAb2J5W