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Re: If |x| < x^2, which of the following must be true?
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01 Dec 2021, 09:00
To answer this, I would suggest first to consider that |x| and x^2 are both ALWAYS POSITIVE.
Next, notice that this is a MUST question, so finding any good NO case (counterexample) will prove it wrong.
I. Given that |x| is defined as sqrt(x^2), then it follows that the number x must be greater than 1 -- that is, the only cases where the square is smaller than the number itself are fractions between 0 and 1. This MUST BE TRUE.
II.
>NO case make x = -2 and we see |-2| = 2 while (-2)^2 = 4
This one doesn't have to be true.
III.
>NO case x = 2 and we see |2| = 2 while 2^2 = 4
This one doesn't have to be true.
The Answer is A.