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[ (√5 +√√5) - (√5 -√√5)]^2 =

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Sunsha
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[ (√5 +√√5) - (√5 -√√5)]^2 = [#permalink] New post   Updated on: 22 Oct 2020, 15:55
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\(( \sqrt{5+\sqrt{5}} - \sqrt{5-\sqrt{5}} )^2\)

A. \(10-4 \sqrt{5}\)

B. \(10-2 \sqrt{5}\)

C. \(20-8 \sqrt{5}\)

D. \(20-4 \sqrt{5}\)

E. \(20 - 2 \sqrt{5}\)


Kudos to right answer !!
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A

Originally posted by Sunsha on 12 Oct 2020, 15:05.
Last edited by Carcass on 22 Oct 2020, 15:55, edited 3 times in total.
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rcpacheco
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Re: [ (√5 +√√5) - (√5 -√√5)]^2 = [#permalink] New post   22 Oct 2020, 15:00
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Sunsha wrote:
Kudos to right answer !!


Let
\(A=\sqrt{5+sqrt(5)}\) and
\(B = \sqrt{5-sqrt(5)}\)

\((A-B)^2 = A^2-2AB+B^2\)

\(A^2+B^2\)=\(5+\sqrt{5}+5-\sqrt{5}=10\)
\(-2AB=-2\sqrt{5^2-5}=-4\sqrt{5}\)

Therefore, \((A-B)^2\) = \(10-4\sqrt{5}\)

Answer is A
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Re: [ (√5 +√√5) - (√5 -√√5)]^2 = [#permalink] New post   22 Oct 2020, 15:51
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The question must be formatted Sir as I edited above.

The images are not allowed on the board but for geometry or DI questions to show the figures

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Re: [ (√5 +√√5) - (√5 -√√5)]^2 = [#permalink] New post   05 Apr 2021, 16:14
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plz expand -2AB properly....
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Re: [ (√5 +√√5) - (√5 -√√5)]^2 = [#permalink] New post   23 Jun 2021, 16:01
I agree, can someone expand -2AB , not sure how to simplify
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[ (√5 +√√5) - (√5 -√√5)]^2 = [#permalink] New post   23 Jun 2021, 19:11
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-2AB = \(-2( \sqrt{5+\sqrt{5}} * \sqrt{5-\sqrt{5}} )\)

\(( \sqrt{a+\sqrt{b}} * \sqrt{a-\sqrt{b}} )\)

\(-2AB=-2\sqrt{a^2-b}\) , it is the same as the expansion of \((a-b)(a+b) = a^2-b^2\)

So,

\(-2AB=-2\sqrt{5^2-5}=-4\sqrt{5}\)

TyJon1 wrote:
I agree, can someone expand -2AB , not sure how to simplify
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Re: [ (5 +5) - (5 -5)]^2 = [#permalink] New post   08 Nov 2023, 15:53
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: [ (5 +5) - (5 -5)]^2 = [#permalink]
08 Nov 2023, 15:53
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