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Is sqrt( (x-3) ^ 2) = 3 - x? (1) x not equal to 3 (2) -x|x|

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Is sqrt( (x-3) ^ 2) = 3 - x? (1) x not equal to 3 (2) -x|x| [#permalink] New post 07 Dec 2007, 19:52
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Is sqrt( (x-3) ^ 2) = 3 - x?

(1) x not equal to 3
(2) -x|x| > 0
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 [#permalink] New post 07 Dec 2007, 20:49
sqrt[ (x-3)^2] has two solutions:
1. x-3 or
2. -(x-3) = 3-x

a. x not equal to 3, the results can be equal if x <3>3. For example: x = 1, sqrt[(x-3)^2] = 2 = 3-x. x = 4, sqrt[(x-3)^2]=1 is not equal to 3-x (3-4=-1). Insuff

b. -x|x| > 0 means that x <0. why? |x| is always positive, thus -x must also be positive. This happens only when x < 0. With x < 0, sqrt[(x-3)^2] will always be equal to 3-x. Sufficient.

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Re: DS: sqrt ( (x-3) ^ 2) = 3 - x? [#permalink] New post 08 Dec 2007, 00:24
eyunni wrote:
Is sqrt( (x-3) ^ 2) = 3 - x?

(1) x not equal to 3
(2) -x|x| > 0


B. since x is -ve, it is always true that sqrt((x-3)^2) = 3 - x.
Re: DS: sqrt ( (x-3) ^ 2) = 3 - x?   [#permalink] 08 Dec 2007, 00:24
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