If x<0, then sqrt(-x|x|) is
(A) -x
(B) -1
(C) 1
(D) x
(E) sqrt(x)
Anyone know the answer to this? An explanation would be great.
square roots and absolute values
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It was my understanding that |x| was the distance along a number line that x was from zero, and since x cannot be a negative distance from zero, |x| had to be a positive number no matter whether x was negative or not? How can |x| be equal to -x?
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your understanding is absolutely correct.Now if we use that logic to get value of |x| we will getaturpening wrote:It was my understanding that |x| was the distance along a number line that x was from zero, and since x cannot be a negative distance from zero, |x| had to be a positive number no matter whether x was negative or not? How can |x| be equal to -x?
|x|=x..when x>0...ex 1,2,3 etc
=0 when x=0
=-x ..when x<0 ..because since sign of x is -ve..if we multiply it with -1 it will give a positive value..ex -1,-2 etc which will make |x| positive
hope this clarifies the confusion
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I would suggest picking numbers.aturpening wrote:It was my understanding that |x| was the distance along a number line that x was from zero, and since x cannot be a negative distance from zero, |x| had to be a positive number no matter whether x was negative or not? How can |x| be equal to -x?
Try X = -2 ( as X<0)
|X| = 2
-X(|X|
-(-2)(2)
= 4
Sqrt (-X(|X|)
4^1/2
2 which is nothing but -X
Pick A
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If x < 0, -x > 0, let's call -x some positive number y, now |x| is also y and y × y = y^2, whose square root is positive [spoiler]y or -x[/spoiler].sumanr84 wrote:This is absurd as |x| is always > 0 ( whether X is <0 or >0)
[spoiler]A[/spoiler]
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Sanjeev K Saxena
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Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com