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# If |x| < x^2, which of the following must be true ?

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Senior Manager
Joined: 04 Aug 2010
Posts: 310
Schools: Dartmouth College
Re: If |x| < x^2, which of the following must be true ?  [#permalink]

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28 Jun 2018, 09:21
1
1
dave13 wrote:
hey GMATGuruNY great explanation ! i have just one question

Algebra:
$$|x| < x^2$$ (as you see $$x^2$$ is without bars / brackets )

$$|x| < |x| * |x|$$ Here you rewrite $$x^2$$as |x| * |x| and not as x*x , can you please explain why ?

many thanks !

$$x^2 = x * x = |x| * |x|$$

For example:
$$3^2 = 3 * 3 = |3| * |3| = 9$$
$$(-3)^2 = -3 * -3 = |-3| * |-3| = 9$$

Given inequality:
$$|x| < x^2$$

Here, I chose to replace x^2 with |x| * |x| so that |x| would appear on both sides, enabling me to divide both sides by |x|:
$$|x| < x^2$$
$$|x| < |x| * |x|$$
$$\frac{|x|}{|x|} < |x| * \frac{|x|}{|x|}$$
$$1 < |x|$$
$$|x| > 1$$
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Joined: 16 Jun 2018
Posts: 10
Re: If |x| < x^2, which of the following must be true ?  [#permalink]

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02 Sep 2018, 17:57
Bunuel wrote:
Skywalker18 wrote:
If |x| < x^2, which of the following must be true ?

A. x > 0
B. x < 0
C. x > 1
D. -1 < x < 1
E. x^2 > 1

Given: $$|x|<x^2$$ --> reduce by $$|x|$$ (side note: we can safely do this as absolute value is non-negative and in this case we know it's not zero too, as if x would be zero inequality wouldn't hold true, so $$|x|>0$$) --> $$1<|x|$$ --> $$x<-1$$ or $$x>1$$.

So we have that $$x<-1$$ or $$x>1$$.

Bunuel can u show how you reached 1<|x|1<|x|
Re: If |x| < x^2, which of the following must be true ? &nbs [#permalink] 02 Sep 2018, 17:57

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