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# X = ?

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Senior Manager
Joined: 21 Jul 2009
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Location: New York, NY
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04 Nov 2009, 13:54
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I'm having some trouble with the formula...
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Intern
Joined: 25 Oct 2009
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Schools: Wharton, HBS, Stanford
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Kudos [?]: 38 [1] , given: 12

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04 Nov 2009, 14:32
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Hi,

try the following approach:

1. Divide both sides by $$(2-sqrt5)$$.

Results in $$x=-\frac{1}{(2-sqrt5)}$$

Skim the answers. There is no any that match. So, modify further

2. Multiply two part of fraction by $$(2+sqrt5)$$ and get

$$x=-\frac{(2+sqrt5)}{(2^2-sqrt5^2)}=-\frac{(2+sqrt5)}{(4-5)}=-\frac{(2+sqrt5)}{(-1)}=2+sqrt5$$

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Senior Manager
Joined: 21 Jul 2009
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Kudos [?]: 110 [0], given: 23

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11 Nov 2009, 07:09
Any known roots formula that is useful in these types of questions?
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11 Nov 2009, 08:10
mendelay wrote:
I'm having some trouble with the formula...
Attachment:
untitled.JPG

Hi I dont know about the formula........but for a quick method just plugin the answer choice and see which answer choice result in the desired value i.e x= -1 in this case..

(2+root 5)*(2-root5)
= 2(2-root5)+root5(2-root5)
=4-2root5+2root5-5
= -1 (root5 gets canceled)

So option A is the correct answer choice
I think this is the quickest method that you can even apply during the real test.
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11 Nov 2009, 08:18
mendelay wrote:
Any known roots formula that is useful in these types of questions?

a tip, whenever i see the square root on the bottom always use the same numbers but change the sign

for example: 1/(2 - sqrt3)

multiply by the same numbers but different sign
(2 + sqrt 3) (1) / (2 - sqrt3)(2+sqrt 3)
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23 Oct 2011, 08:07
In case of surds, try to multiply with the conjugate of the given no. If a+sqrt(b) is given multiply with a-sqrt(b) and vice-versa.

That will lead to the formula (a^2)-(b^2) and it can be solved further from here.
As above, 2-sqrt5 is there, multiply by 2+sqrt5. (Just change the sign and multiply). This helps to eliminate the sqrt part.
Re: X = ?   [#permalink] 23 Oct 2011, 08:07
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