prachich1987 wrote:If root of (x+4)^2 = 3, which of the following could be the value of x - 4?

-11
-7
-4
-3
5


[spoiler]The OA is -11.But I have read somewhere that on GMAT you should never consider -ve roots & always you have to consider the positive roots.
Then why is the OA, -11 here?[/spoiler]

If root of [spoiler](x+4)^2 = 3[/spoiler]

anshumishra wrote:

prachich1987 wrote:If root of (x+4)^2 = 3, which of the following could be the value of x - 4?

-11
-7
-4
-3
5


[spoiler]The OA is -11.But I have read somewhere that on GMAT you should never consider -ve roots & always you have to consider the positive roots.
Then why is the OA, -11 here?[/spoiler]

This part looks incomplete :

If root of [spoiler](x+4)^2 = 3[/spoiler]

what ?
It is like :
If root of an equation in x (something else should be here), which of the following could be the value of x - 4 ?

By the way, GMAT says never consider -ve root when taking square root :
So [sqrt(25)] = 5, but not -5. why ?
if sqrt[25] = sqrt [-5]* sqrt [-5] ; sqrt of -ve number leads to imaginary numbers, which GMAT doesn't test.

prachich1987 wrote:

anshumishra wrote:

prachich1987 wrote:If root of (x+4)^2 = 3, which of the following could be the value of x - 4?

-11
-7
-4
-3
5


[spoiler]The OA is -11.But I have read somewhere that on GMAT you should never consider -ve roots & always you have to consider the positive roots.
Then why is the OA, -11 here?[/spoiler]

This part looks incomplete :

If root of [spoiler](x+4)^2 = 3[/spoiler]

what ?
It is like :
If root of an equation in x (something else should be here), which of the following could be the value of x - 4 ?

By the way, GMAT says never consider -ve root when taking square root :
So [sqrt(25)] = 5, but not -5. why ?
if sqrt[25] = sqrt [-5]* sqrt [-5] ; sqrt of -ve number leads to imaginary numbers, which GMAT doesn't test.

Oh I apologize for making above typo error
I have edited the question
Plz refer to the edited question

anshumishra wrote:

prachich1987 wrote:

anshumishra wrote:

prachich1987 wrote:If root of (x+4)^2 = 3, which of the following could be the value of x - 4?

-11
-7
-4
-3
5


[spoiler]The OA is -11.But I have read somewhere that on GMAT you should never consider -ve roots & always you have to consider the positive roots.
Then why is the OA, -11 here?[/spoiler]

This part looks incomplete :

If root of [spoiler](x+4)^2 = 3[/spoiler]

what ?
It is like :
If root of an equation in x (something else should be here), which of the following could be the value of x - 4 ?

By the way, GMAT says never consider -ve root when taking square root :
So [sqrt(25)] = 5, but not -5. why ?
if sqrt[25] = sqrt [-5]* sqrt [-5] ; sqrt of -ve number leads to imaginary numbers, which GMAT doesn't test.

Oh I apologize for making above typo error
I have edited the question
Plz refer to the edited question

So now we can write the equation as :

sqrt [(x+4)^2] = 3

=> |x+4| = 3
=> x = -7 or -1
So, x-4 = -11 or -5

-11 is the only option given.

prachich1987 wrote:

anshumishra wrote:

prachich1987 wrote:

anshumishra wrote:

prachich1987 wrote:If root of (x+4)^2 = 3, which of the following could be the value of x - 4?

-11
-7
-4
-3
5


[spoiler]The OA is -11.But I have read somewhere that on GMAT you should never consider -ve roots & always you have to consider the positive roots.
Then why is the OA, -11 here?[/spoiler]

This part looks incomplete :

If root of [spoiler](x+4)^2 = 3[/spoiler]

what ?
It is like :
If root of an equation in x (something else should be here), which of the following could be the value of x - 4 ?

By the way, GMAT says never consider -ve root when taking square root :
So [sqrt(25)] = 5, but not -5. why ?
if sqrt[25] = sqrt [-5]* sqrt [-5] ; sqrt of -ve number leads to imaginary numbers, which GMAT doesn't test.

Oh I apologize for making above typo error
I have edited the question
Plz refer to the edited question

So now we can write the equation as :

sqrt [(x+4)^2] = 3

=> |x+4| = 3
=> x = -7 or -1
So, x-4 = -11 or -5

-11 is the only option given.

Sorry But I don't understand why we are considering -ve root here
why don't we simply take x+4 as an only root

Anurag@Gurome wrote:

prachich1987 wrote:Sorry But I don't understand why we are considering -ve root here
why don't we simply take x+4 as an only root

Hi prachihi1987!

We are not considering negative roots here. In fact we're considering only positive roots by taking the square root as |x + 4|. Let's see how?

As x is a variable, we don't know what could be the value of x. Thus we don't know whether (x + 4) is positive or negative. Now if we take √(x + 4)² = (x + 4), then for any x > -4, (x + 4) is positive and the result is okay. But for x < -4, (x + 4) is negative! Thus for any x < -4, we are making a mistake! Let's take an example. Say x = -6 => (x + 4) = -2. This means for x = -6, according to our assumption √(x + 4)² = (x + 4), √(-6 + 4)² = (-6 + 4) = -2 => A negative square root!

What you mentioned earlier "on GMAT you should never consider -ve roots & always you have to consider the positive roots" is correct. That's why we take |x| as the value of √(x)² which ensures only non-negative roots for any value of x. Thus in this case we must take √(x + 4)² = |x + 4|.

From your post I think you have a misconception about |x|. |x| can never be a negative quantity! By definition |x| = x for x ≥ 0 and |x| = -x, for x < 0. Note that although we are using +ve and -ve signs both, we are considering only the positive values! As for positive x, |x| = x => positive and for negative x, |x| = -x => positive (As putting a minus sign before a negative value makes it positive!)

Thus if we consider |x + 4| as the value of √(x + 4)², we are considering only the positive root! In fact we are ensuring that the root is positive by taking the absolute value.