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Am I right in that the square root of X^2 is absolute value of x if we don't know whether x is negative or positive? Therefore, if we knew that x is negative, the square root of X^2 is -x? Thanks.

My understanding is the SQRT(x^2) = |x| since the square of an unknown yields +/- results. Therefore if x<0 then SQRT(x^2) is x=-a. Are you saying that a=-x?

x can have two values : +1 and -1 (that is logical) or only one value : +1 x^2=1 ==> x = sqr. root(1) = 1...

.Got confused because in Kaplan it is mentioned as 2 values and I had read somewere in GMAT these equations have absolute values.

2) x^4 = 1

Here definitely x will have 2 values : +1, -1

But not sure about the 1st case... Please enlighten the GMAT logic on this...

x^2 =1 ==> x = +1,-1
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Not sure this is GMAT logic or more general math logic, but here goes...

Lets say we investigate some squares: 1, 4, 9, 16, etc... Well how can we create these squares? For 1: (1)^2 OR (-1)^2, For 4: (2)^2 OR (-2)^2, etc...

Well when we undo the squares by taking the square root function then we create 2 solutions since there are 2 ways to make a square, ie 9 can be made by (3)^2 or (-3)^2. These returns are similar to absolute value function, since absolute value is basically distance on a number line AND all distances are positive. Since there are 2 ways to go on a number line (left or right) we have 2 solution possibilities for the absolute value. Therefore sqrt(x^2)=|x|. Hope that helps.

yes it is...go to gmat club math book and look at the chapter of inequalitites...explicitly states so...
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