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For which of the following inequalities is x^2 - 2<-1

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For which of the following inequalities is x^2 - 2<-1  [#permalink]

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New post Updated on: 18 Jul 2014, 07:15
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A
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D
E

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Question Stats:

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For which of the following inequalities is x^2 - 2 < -1 ?

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

I solved the equation as
=> x^2 - 2 +1 <0
=> x^2 -1 <0
=> (x+1)(x-1) < 0
x+1 < 0 or x-1<0
x< -1 or x < 1

I am not sure what am I doing wrong

Originally posted by ashutoshbarawkar on 17 Jul 2014, 19:49.
Last edited by Bunuel on 18 Jul 2014, 07:15, edited 2 times in total.
Edited the question.
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Re: For which of the following inequalities is x^2 - 2<-1  [#permalink]

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New post 17 Jul 2014, 20:05
1
ashutoshbarawkar wrote:
For which of the following inequalities is x^2 - 2<-1
a. x<1
b. x<-1
c. x<0
d. -1<x<1
e. x<-1 or x>1




I solved the equation as
=> x^2 - 2 +1 <0
=> x^2 -1 <0
=> (x+1)(x-1) < 0
x+1 < 0 or x-1<0
x< -1 or x < 1

I am not sure what am I doing wrong


Hello Ashutosh,

The given equation can be written as\(x^2< 1\)

Now since \(x^2\geq{0}\) therefore both LHS and RHS are non-negative

So taking squareroot we get

\(\sqrt{x^2} <1\)

Important Property of Mod \(\sqrt{x^2} =|x|\)

So we have |x|< 1 or -1<x<1

Ans is D.

The question can also be done using graphical approach. Check out the below link for a similar problem.

if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html

Have a look at the below links for easy navigation on Gmatclub

rules-for-posting-please-read-this-before-posting-133935.html#p1092822
all-you-need-for-quant-140445.html#p1130136
new-to-the-gmat-club-start-here-130870.html
gmat-prep-software-analysis-and-what-if-scenarios-146146.html

ATB
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Re: For which of the following inequalities is x^2 - 2<-1  [#permalink]

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New post 17 Jul 2014, 21:01
Thanks for the explanation.

I am still confused about why the method I am using is wrong.

(x-1)(x+1)<0
x-1<0 or x+1<0
x<1 or x<-1
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Re: For which of the following inequalities is x^2 - 2<-1  [#permalink]

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New post 17 Jul 2014, 23:06
ashutoshbarawkar wrote:
Thanks for the explanation.

I am still confused about why the method I am using is wrong.

(x-1)(x+1)<0
x-1<0 or x+1<0
x<1 or x<-1


Okay...If you look at the graphical method you can understand better..Having said that let's test some values

We have (x-1)(x+1)<0
So x=-1 and x=1

Now Let's take x=2 and see what happens to the expression
We get (2-1)(2+1)<0 or 3<0 which is incorrect.

So we need to identify a region where the above equation holds good.
Consider x=0, the expression is -1<0 Yes.

Consider x=-2, the expression is (-2-1)(-2+1) <0 or 3<0. No

Thus the only range where the equations holds good is -1<x<1...

Check out the solution in the link I shared above. It will answer your queries.
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Re: For which of the following inequalities is x^2 - 2<-1  [#permalink]

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New post 25 Jun 2016, 23:53
\(x^2 - 2 < -1\) when \(x^2 - 1 < 0\); in other words, \((x-1)*(x+1) < 0\)

So x-1 has to be smaller than 0 and x+1 has to be greater than 0. In other words, \(-1<x<1\)

Answer choice D.
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Re: For which of the following inequalities is x^2 - 2<-1   [#permalink] 25 Jun 2016, 23:53

For which of the following inequalities is x^2 - 2<-1

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