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Senior Manager
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X = ? [#permalink]

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New post 04 Nov 2009, 13:54
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I'm having some trouble with the formula...
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New post 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

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

The answer should be A.
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New post 11 Nov 2009, 07:09
Any known roots formula that is useful in these types of questions?
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New post 11 Nov 2009, 08:10
mendelay wrote:
I'm having some trouble with the formula...
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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..

A is the clear answer

(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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New post 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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New post 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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