If |x^2 − 12| = x, which of the following could be the value of x?

Another easy way and time-saver will be to substitute the values directly in the equation.
so
A: |(-4)^2-12|=|4| ne -4 => FALSE
B: |(-3)^2-12|=|-3| ne -3 => FALSE
C: |(1)^2-12|=|-11| ne -1 => FALSE
D: |(2)^2-12|=|-8| ne 2=> FALSE
E: |(3)^2-12|=|-3| eq 3 => TRUE

Substituting the value works in most of the Problems of GMAT and is a sureshot way...

Same opinion , answer will be (E)

\(|x^2 − 12| = x\)
\(|x^2 − 12|\)cannot be negative; anything that comes out of mod is always positive
so \(|x^2 − 12|>0\)

Out of our options A= -4 B= -3 cannot be the right answer because none of them are greater than 0

Now only Option C=1 or D=2 or E=3 are contenders for right answers.

A quick Cursory crude calculation will tell you that E is the right choice
\(|-3^2-12|=3\)

\(|9-12|=3\)

\(|-3|=3\)

\(3=3\)

ANSWER IS E

Hi chetan2u,

Though I know the substitution method, but instinctively I went to solve the the equations given.

Can you help me how it can be done with critical value method. I am stuck up.

Can you tell me the algebraic way?

I am stuck up a bit.

QZ

Since we see that the left side of the equation must be positive, the right side also must be positive.

Thus, A and B cannot be correct since the absolute value of any quantity can’t be negative. Let’s substitute in the remaining answer choices:

|1^2 - 12 | = 1 ?

We see this is not true.

|2^2 - 12| = 2 ?

We see this is not true

|3^3 - 12| = 3 ?

We see this is true.

Answer: E

I'll help.

First of all, x is the outcome of an absolute value so x=>0

Then we have to analyze the two possible scenarios of what we have inside the absolute value so that we can eliminate the absolute value:

1. X^2-12=>0, x^2=>12
So that x=<-sqrt(12) or x=>sqrt(12)
The only possible scenario according to the constraint that x can take any non negative value is the second one so we can say that x has to be greater than or equal to approximately 3.4

Then we would have the quadratic equation x^2-x-12=0 with roots x=-3 or x=4 we eliminate the first one because x can not take negative values.

2. X^2-12<0, x^2<12
So that -sqrt(12)<x<sqrt(12)
Then according to the initial constraint 0<x<3.4

Then we would have the quadratic equation x^2+x-12=0 with roots x=3 or x=-4
We eliminate the second one because x can not take negative values.

So from the first scenario x=4 and from the second one x=3, those are the two solutions for the absolute value equation.

I hope it is clear.

Regards

César Orihuela

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Thanks Cesar to clarify.

Posted from my mobile device

The algebraic way:

|x^2 − 12| = x

Case 1:

x^2 - 12 = x

x^2 - x = 12

x (x - 1) = 12

We need two consecutive numbers whose products is 12.

So 4(4-1) = 12

4*3 = 12

But we don't have "4" in the answer choices.

Case 2:

x^2 - 12 = -x

x^2 + x = 12

x (x + 1) = 12

We need two consecutive numbers whose products is 12.

3 (3 + 1) = 12

3*4 = 12

12 = 12

So x = 3

(E)

Hello, is there any algebraic way to solve this? can u plz explain

Posted from my mobile device

HERE IT IS:

https://gmatclub.com/forum/if-x-2-12-x- ... l#p2052961

Please read the complete thread before raising queries. Hope this helps.

QZ

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