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# What is the value of x?

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Manager
Joined: 15 Dec 2015
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What is the value of x?  [#permalink]

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Updated on: 15 Mar 2019, 04:21
4
3
00:00

Difficulty:

85% (hard)

Question Stats:

39% (01:20) correct 61% (01:30) wrong based on 135 sessions

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What is the value of x?

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

(2) x is not equal to 1.

Originally posted by DHAR on 30 Aug 2017, 17:09.
Last edited by Bunuel on 15 Mar 2019, 04:21, edited 1 time in total.
Updated.
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Joined: 02 Aug 2009
Posts: 7977
Re: What is the value of x?  [#permalink]

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30 Aug 2017, 20:12
3
1
DH99 wrote:
What is the value of x?

1. √ x = x-2

2. x is not equal to 1.

Hi..

1) √x=x-2
Square both sides
$$x=x^2-4x+4.....x^2-5x+4=0....x^2-4x-x+4=0.........(x-4)(x-1)=0$$
So x can be 4 or 1..
Substitute in equation and see if values are valid.
A) 2
√4=4-2=2.... Valid
B) 1
√1=1-2=-1..... Not valid
SQUARE Root has to be POSITIVE

Only possible value :- 4
Sufficient

2) X is not 1..
Nothing much.
But only to tempt you to click C....the C trap
Insufficient
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Re: What is the value of x?  [#permalink]

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24 Sep 2017, 17:41
chetan2u wrote:
DH99 wrote:
What is the value of x?

1. √ x = x-2

2. x is not equal to 1.

Hi..

1) √x=x-2
Square both sides
$$x=x^2-4x+4.....x^2-5x+4=0....x^2-4x-x+4=0.........(x-4)(x-1)=0$$
So x can be 4 or 1..
Substitute in equation and see if values are valid.
A) 2
√4=4-2=2.... Valid
B) 1
√1=1-2=-1..... Not valid
SQUARE Root has to be POSITIVE

Only possible value :- 4
Sufficient

2) X is not 1..
Nothing much.
But only to tempt you to click C....the C trap
Insufficient

Thanks Chetan

Answer to this question teach us a very good lesson. Whenever we are doing squire on both the sides of the equation to solve it, always check putting the solution back into the equation to see if the value really satisfy the original equation.

For example, in this case by solving (by squiring both the sides) equation given in option 1, we get solution as 1 and 4, however putting back the value in the original equation clearly shows value=1 do not satisfy the original equation.

The reason for this is that for the simplicity we are doing squire on both the sides, but mathematically it produced a fundamentally different equation as compared to the original equation.
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Re: What is the value of x?  [#permalink]

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16 Oct 2018, 10:32
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Re: What is the value of x?   [#permalink] 16 Oct 2018, 10:32
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