Hate to beat a dead horse, but I think the explanation that -x is the answer because "the question says x<0" is wrong. While -x is indeed the answer, the explanation is wrong and the logic faulty.
The real issue here is one of translation. You CANNOT rephrase sqrt(-x lxl) as sqrt(-(-x) lxl). The reason is because you have simply inserted a negative sign in front of the "x." The value of x will will still be a negative number.
A better translation is this: x = -y where y is a positive number.
Sqrt(-(-y) l-yl) gives you sqrt(y^2), which in turn gives you y. Since the equality we set up was x = -y, it is also true that y = -x. Thus, the answer is -x.
Some people have already said something similar in this thread, but they seemed to have been ignored so I thought I would reiterate.
The real issue here is one of translation. You CANNOT rephrase sqrt(-x lxl) as sqrt(-(-x) lxl). The reason is because you have simply inserted a negative sign in front of the "x." The value of x will will still be a negative number.
A better translation is this: x = -y where y is a positive number.
Sqrt(-(-y) l-yl) gives you sqrt(y^2), which in turn gives you y. Since the equality we set up was x = -y, it is also true that y = -x. Thus, the answer is -x.
Some people have already said something similar in this thread, but they seemed to have been ignored so I thought I would reiterate.
