m7373 wrote:How does - x | x | > 0 result in x<0 ? I don't understand.

joshi.komal wrote:Hi Hemanth,

Which part you did not understand? ...

I see some confusions let me try again :

Question : Is sqrt of (x-3)^2 = 3-x ?
Solution: Since we know sqrt of (x-3)^2 = either +(x-3) or - (x-3)

But sqrt of (x-3)^2 will be = 3-x only when when sqrt(x-3)^2 = - (x-3)

Now simplify the question:
sqrt(x-3)^2 = - (x-3) (It is a negative root of the no so use the inequality)
or x-3 < 0
or x < 3
So our rephrased question:
Is x <3 ?

Now look at the statements:

(1) x is not equal to 3: Since this statement is not giving us any info about whether x <3> 0
From this we can say x < 0
Since 0(Zero) < 3
So we can say x <3>0
2)Sqrt of (x-3)^2 =-(x-3) if x-3<0

i am not sure if your assumption is right or i am not sure if i am missing something.

becasue sqrt of (16) =+4 or -4.
and there is no condition attached to it.Thinking in similar terms,
Sqrt of (x-3)^2 can be always be either +(x-3) or -(x-3).

Thanks,
Hemant Maddineni.

horizonx29 wrote:The answer is A.

x = 3 is the only value for x that makes the question true. So A tells x can't equal three. Therefore if we take A to be true, that sufficient to tell us that the answer to their question is no.

The prior responses forget that the sqrt has +/- roots. You're assuming the roots are + only.