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If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll

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If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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Tough and Tricky questions: Algebra.



If \(\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}\), then x could be equal to which of the following?

A. -1
B. 0
C. 1
D. 4
E. cannot be determined.

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[Reveal] Spoiler: OA

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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Algebra.



If \(\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}\), then x could be equal to which of the following?

A. -1
B. 0
C. 1
D. 4
E. cannot be determined.

Kudos for a correct solution.


\(\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}\)

squaring both sides we have

4 + x^1/2= x+2
=x-x^1/2-2
let x^1/2=k
x= (x^1/2)^2 = k^2

k^2-k-2=0
k^2-2k+k-2=0
k(k-2)+1(k-2)
(k+1)(k-2)=0
k=-1 or k=2
or x^1/2=-1 or x^1/2=2
x^1/2=-1 is not possible. as square root of x will be positive.
thus x^1/2 = 2
squaring both sides we have
x=4
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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New post 06 Nov 2014, 12:59
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No need to solve...just put the options one by one and check. Only 4 make sense . LHS=RHS
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Algebra.



If \(\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}\), then x could be equal to which of the following?

A. -1
B. 0
C. 1
D. 4
E. cannot be determined.

Kudos for a correct solution.



Plug in the choices in place of x

We need LHS = RHS

Only 4 makes the LHS = RHS

So answer is D
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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New post 06 Nov 2014, 21:46
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√(4 + x^1/2) =√(x + 2)

squaring both sides..

4 + x^1/2 = x+2
x^1/2 - x-2

SBS again..

x = x^2 +4 - 4x
x=1,4

can not be determined.

But if we plug in the values, x = 4.. clear answer.

Bunuel, please tell me where I am lacking in terms of approach.

Thanks!
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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2013gmat wrote:
√(4 + x^1/2) =√(x + 2)

squaring both sides..

4 + x^1/2 = x+2
x^1/2 - x-2

SBS again..

x = x^2 +4 - 4x
x=1,4

can not be determined.

But if we plug in the values, x = 4.. clear answer.

Bunuel, please tell me where I am lacking in terms of approach.

Thanks!



Yes your method is correct...

I had made a mistake once and i forgot to plug in the values of X in the equation.

Here You have to plug in the values of X =1,4 in the equation to check its validity.

If X=1 then LHS is not equal to RHS, Hence not valid
If X=4 then LHS = RHS, Hence Valid
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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\(\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}\)

Squaring both sides

\(4 + x^{\frac{1}{2}} = x+2\)

\(x - \sqrt{x} = 2\)

Only for x = 4, the above equation would hold true

Answer = D
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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New post 09 Nov 2014, 20:02
2013gmat wrote:
√(4 + x^1/2) =√(x + 2)

squaring both sides..

4 + x^1/2 = x+2
x^1/2 - x-2

SBS again..

x = x^2 +4 - 4x
x=1,4

can not be determined.

But if we plug in the values, x = 4.. clear answer.

Bunuel, please tell me where I am lacking in terms of approach.

Thanks!



This is correct. However, after obtaining values of x = 1,4, we require to return back to the "original equation" to check the feasibility

For x = 1 will have LHS NOT equal to RHS

For x = 4, LHS = RHS which holds true
So, answer = D
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If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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New post 14 Dec 2014, 09:00
x=4 makes sense only after ignoring the possibility that sqrt(4) = -2. In the same sense, option C (x=1) also correct if we consider the situation that sqrt(1)= -1 . This is definitely not a 700 level question, but surely a controversial one.
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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New post 05 Jan 2015, 12:10
I also used the same way as Paresh. Worked pretty fast. Less than 1 min for sure.
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If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of th [#permalink]

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New post 28 Apr 2015, 23:56
As far as I know, \(x^{1/2}\), can yield both +ve and -ve roots, unlike \(\sqrt{x}\) where only positive roots are possible.

If the OA is correct then the question should be modified to replace \(x^{1/2}\) by \(\sqrt{x}\).
Or the OA should be changed to E.

Bunuel, could you please help to comment?
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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New post 04 May 2015, 18:32
Hi shreyast,

I think that you're confusing one rule with another.

If you're given X^2 = 16, then there ARE 2 solutions: +4 and -4

If you're given X^(1/2) = √X = 16, then there is just ONE solution: +4

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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal [#permalink]

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New post 15 Jun 2015, 02:49
PareshGmat wrote:
\(\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}\)

Squaring both sides

\(4 + x^{\frac{1}{2}} = x+2\)

\(x - \sqrt{x} = 2\)

Only for x = 4, the above equation would hold true

Answer = D


Hi Paresh
Could you kindly show me how you would solve the equiton the get the final possible values of X?
Thank you
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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New post 15 Jun 2015, 02:56
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reto wrote:
PareshGmat wrote:
\(\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}\)

Squaring both sides

\(4 + x^{\frac{1}{2}} = x+2\)

\(x - \sqrt{x} = 2\)

Only for x = 4, the above equation would hold true

Answer = D


Hi Paresh
Could you kindly show me how you would solve the equiton the get the final possible values of X?
Thank you


\(x - \sqrt{x} = 2\);

\(x - \sqrt{x} -2= 0\);

\((\sqrt{x})^2 - \sqrt{x} -2= 0\);

Solve quadratic for \(\sqrt{x}\):

\(\sqrt{x}=-1\) (discard since the square root of a number cannot be negative) or \(\sqrt{x}=2\).
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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New post 08 Mar 2016, 09:09
manpreetsingh86 wrote:
Bunuel wrote:

Tough and Tricky questions: Algebra.



If \(\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}\), then x could be equal to which of the following?

A. -1
B. 0
C. 1
D. 4
E. cannot be determined.

Kudos for a correct solution.


\(\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}\)

squaring both sides we have



4 + x^1/2= x+2
=x-x^1/2-2
let x^1/2=k
x= (x^1/2)^2 = k^2

k^2-k-2=0
k^2-2k+k-2=0
k(k-2)+1(k-2)
(k+1)(k-2)=0
k=-1 or k=2
or x^1/2=-1 or x^1/2=2
x^1/2=-1 is not possible. as square root of x will be positive.
thus x^1/2 = 2
squaring both sides we have
x=4



Very Very lengthy
Just plug in the values..
it will spare some tim :)
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If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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New post 11 Aug 2016, 08:36
Hi Guys,

When we square both sides of the equation, isn't the result in the absolute value form? such as --> l 4 + x^1/2 l = l x + 2 l ? I am confused with this. As (√x)^2 = lxl since we don't know if x is positive or negative. Why this rule is not applied here?

Thanks for your help!
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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New post 11 Aug 2016, 10:51
HarveyKlaus wrote:
Hi Guys,

When we square both sides of the equation, isn't the result in the absolute value form? such as --> l 4 + x^1/2 l = l x + 2 l ? I am confused with this. As (√x)^2 = lxl since we don't know if x is positive or negative. Why this rule is not applied here?

Thanks for your help!

Hi
Why are you using the absolute value theory here
Just plug in the options.
and to point out => x has to be positive here as x^1/2 is √x which cant be -ve in the gmat maths

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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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How do we know when to try feeding in the values from given options and when to solve the equation to derive the value of x? :?:
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If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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New post 19 Jan 2017, 04:42
sadhvisood wrote:
How do we know when to try feeding in the values from given options and when to solve the equation to derive the value of x? :?:


I would say , you could only decide this by looking at the question.

\(\sqrt{4 + x^1/2}\) = \(\sqrt{x + 2}\)

First thing you should remember seeing a square root is that the variable under square root can never be negative.so if you know this fact you can straight away get away with the first option.
Now ask yourself whether you want to solve this equation as it has \(\sqrt{x}\) and x as variable - so you are talking about a quadratic equation.

now look at the answer choices : its easier to substitute and check the values

[B] 0 : 2 =\(\sqrt{2}\) ; not true
[C] 1 : \(\sqrt{5}\) = \(\sqrt{3}\) ; not true
[D] 4 : \(\sqrt{6}\) = \(\sqrt{6}\) - bingo! no need to check option E
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll [#permalink]

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New post 19 Jan 2017, 15:35
Square on both sides
4 + x^1/2 = x + 2
4 + \(\sqrt{x}\) = x + 2
4 - 2 = x - \(\sqrt{x}\)
2 = x - \(\sqrt{x}\)
Again square on both sides
4 = x^2-x
4 = x(x-1)
Either x = 4 or x = 5
D

Bunuel is this a right approach?Thanks
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll   [#permalink] 19 Jan 2017, 15:35

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