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
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if x<0, then (-x|x|)^1/2 is what?
Source: Beat The GMAT — Problem Solving |
since x<0
-x>0
take x=-3 for example and plug in:
sqrt(-(-3)|3|)= sqrt (3*3)= 3
so answer is -x.
A
-x>0
take x=-3 for example and plug in:
sqrt(-(-3)|3|)= sqrt (3*3)= 3
so answer is -x.
A
I don't understand what we need to find here X or the result of equation root(-X*|X|). Please explain me.
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!!
