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DS question

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magical cook Master | Next Rank: 500 Posts Default Avatar
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DS question

Post Wed Feb 14, 2007 9:49 am
Hi

The attached question's answer is D. But I have two things that I did not understand...

1) in OG, it says √(x-5)^2 = lx-5l ,therefore, lx-5l=5-x.

But I thought, if √(x-5)^2 = 5-x, then we can make both sides squared and it will be (x-5)^2 = (5-x)^2. Can you explain why we can not both sides squared ???


2) for the first condition, -xlxl>0, but I don't get what this means....


Thanks again.
Rina Very Happy
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amitamit2020 Junior | Next Rank: 30 Posts Default Avatar
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24 Jan 2007
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Post Wed Feb 14, 2007 10:44 am
Rina,

Heare are my thoughts,

1) there is no inconsistancy in saying (5 - x)^2 = (X - 5)^2 it is perfectly ok .. to be more clear assume a value of X say 3, you will have 5 - x = 5 - 3 = 2 and x - 5 = 3 - 5 = -2; now squar both the things ou will get (2^2) = ((-2)^2) = 4

2) -x * |x| > 0 means that x < 0 because we have |x| which is always positive or zero. Now that means - x has to be positive in order to satisfy the given condition. so x is negative i.e. x < 0

for the given question X < 0 < 5 means that x - 5 < 0

now |X - 5| = - (x - 5) .. if (x-5 < 0 ... (from definition of mode)

so |x - 5 | = 5 - x .. thus statement (2) alone is also sufficinet to answer the question.

Hope it clarifies.

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