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if x<0, then (-x|x|)^1/2 is what?
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tohellandback
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since X is negative
|x|=-x
sqrt(-x|x|)= sqrt(-x*-x)=sqrt(x^2)=|x|=-x
Answer A
sqrt(x^2) = |x| is a rule
|x|=-x
sqrt(-x|x|)= sqrt(-x*-x)=sqrt(x^2)=|x|=-x
Answer A
sqrt(x^2) = |x| is a rule
The powers of two are bloody impolite!!
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ogbeni
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GambitOS
On the GMAT, the square root of a number is ALWAYS positive but when you have x^2, x could be positive or negative. In other words,
(x)^1/2 = x
(x)^2 = x or -x
This is a statement of fact from the Official Guide.
Now consider what Matmasi contributed:
since x<0, -x>0
Therefore, the square root of |x| multiplied by -(-x) = x (and remember that on the GMAT square roots are ALWAYS positive).
Remember Matmasi already noted that -x>0, and when you plug in the value of -3 as x into -x you have -(-3) = 3. Therefore -x = 3.
Follow the logic and it will make sense.
Thanks tohellandback and matmasi. This forum rocks!!
On the GMAT, the square root of a number is ALWAYS positive but when you have x^2, x could be positive or negative. In other words,
(x)^1/2 = x
(x)^2 = x or -x
This is a statement of fact from the Official Guide.
Now consider what Matmasi contributed:
since x<0, -x>0
Therefore, the square root of |x| multiplied by -(-x) = x (and remember that on the GMAT square roots are ALWAYS positive).
Remember Matmasi already noted that -x>0, and when you plug in the value of -3 as x into -x you have -(-3) = 3. Therefore -x = 3.
Follow the logic and it will make sense.
Thanks tohellandback and matmasi. This forum rocks!!
