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I have a simple doubt? Maybe a but lame.. but I need to know

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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I have a simple doubt? Maybe a but lame.. but I need to know

by nk_81 » Fri Dec 24, 2010 11:34 am
If we have an equation (x+1) sqr = x sqr

We can get
x sqr + 2x + 1 = x sqr
hence x = -1/2

but why can't we perform a square root on both sides and end up with an equation

x + 1 = x

which doesn't make sense but technically is doable.... AM I MISSING SOME SIMPLE FUNDAMENTAL RULE?
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by stormier » Fri Dec 24, 2010 12:03 pm
nk_81 wrote:If we have an equation (x+1) sqr = x sqr

We can get
x sqr + 2x + 1 = x sqr
hence x = -1/2

but why can't we perform a square root on both sides and end up with an equation

x + 1 = x

which doesn't make sense but technically is doable.... AM I MISSING SOME SIMPLE FUNDAMENTAL RULE?
squareroot of 4 is either +2 or -2

so square root of (x+1)^2 could be either +(x+1) or -(x+1). So you cannot simply take the positive roots on both sides of the equation and equate them.
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by anshumishra » Fri Dec 24, 2010 12:07 pm
nk_81 wrote:If we have an equation (x+1) sqr = x sqr

We can get
x sqr + 2x + 1 = x sqr
hence x = -1/2

but why can't we perform a square root on both sides and end up with an equation

x + 1 = x

which doesn't make sense but technically is doable.... AM I MISSING SOME SIMPLE FUNDAMENTAL RULE?
This is not the right forum for this question. Hopefully the moderators will move the topic.

I am using an example to point out the flaw :
25 = 25
=> (5)^2 = (-5)^2
If you take a square root both the sides and conclude 5 = -5, that is wrong.

Sqrt (x^2) = |x| (As square root should always be a non-negative value)
So using that if you'll solve the equation you have mentioned, it will reduce to :

|x+1| = |x|

And then you will get the same answer.
Thanks
Anshu

(Every mistake is a lesson learned )
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by nk_81 » Wed Dec 29, 2010 2:36 am
Ok...here is another fundamental doubt...
Q- If m and n are both positive, what is the value of m(sqr root n)?
1) mn/sqr root n = 10
2) m sqr.n/2=50

Now my approach says
1) sufficient - mn/sqr rt n can be written as
(m . sqr rt n. sqr rt n)/ sqr rt n ,
cancel sqr rt n from both nr and dr
and u have what the question is asking.
Am i right? because i find that this is what came to my mind first but this has not been described in Kaplan. I am doubting my approach.
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by stormier » Wed Dec 29, 2010 5:50 am
nk_81 wrote:Ok...here is another fundamental doubt...
Q- If m and n are both positive, what is the value of m(sqr root n)?
1) mn/sqr root n = 10
2) m sqr.n/2=50

Now my approach says
1) sufficient - mn/sqr rt n can be written as
(m . sqr rt n. sqr rt n)/ sqr rt n ,
cancel sqr rt n from both nr and dr
and u have what the question is asking.
Am i right? because i find that this is what came to my mind first but this has not been described in Kaplan. I am doubting my approach.
That is correct - your reasoning is fine. 1) is sufficient; 2) insufficient - hence A.
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by nk_81 » Wed Dec 29, 2010 9:22 am
Thank You
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by nk_81 » Wed Dec 29, 2010 9:26 am
Actually stormier.... The answer is D, both are sufficient.

Take the square of the Question stem equation, you get (m sqr).n

Which is what you get with the second choice too.
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by stormier » Wed Dec 29, 2010 3:04 pm
nk_81 wrote:Actually stormier.... The answer is D, both are sufficient.

Take the square of the Question stem equation, you get (m sqr).n

Which is what you get with the second choice too.
Thanks for correcting me. D is the right answer, of course. I have a hard time reading the sqr and sqr root notations. I wish they added superscripts and subscripts tools.
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by lunarpower » Sun Jan 02, 2011 1:26 am
nk_81 wrote:If we have an equation (x+1) sqr = x sqr

We can get
x sqr + 2x + 1 = x sqr
hence x = -1/2

but why can't we perform a square root on both sides and end up with an equation

x + 1 = x

which doesn't make sense but technically is doable.... AM I MISSING SOME SIMPLE FUNDAMENTAL RULE?
yep
the square root of x^2 is |x|, not x. similarly, for any other quantity, the square root of (quantity)^2 is |quantity|, not just "quantity".

so, when you take the square root of both sides, you get |x + 1| = |x|, an equation that is indeed satisfied by the value x = -1/2.
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