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# (1+5^1/2)(1-5^1/2)=

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Math Expert
Joined: 02 Sep 2009
Posts: 55618

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02 Jan 2014, 06:40
1
6
00:00

Difficulty:

5% (low)

Question Stats:

90% (00:22) correct 10% (00:50) wrong based on 921 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

$$(1+\sqrt{5})(1-\sqrt{5})=$$

(A) -4
(B) 2
(C) 6
(D) $$-4-2\sqrt{5}$$
(E) $$6-2\sqrt{5}$$

Problem Solving
Question: 20
Category: Arithmetic Operations on radical expressions
Page: 64
Difficulty: 500

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Math Expert
Joined: 02 Sep 2009
Posts: 55618

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02 Jan 2014, 06:42
SOLUTION

$$(1+\sqrt{5})(1-\sqrt{5})=$$

(A) -4
(B) 2
(C) 6
(D) $$-4-2\sqrt{5}$$
(E) $$6-2\sqrt{5}$$

Apply $$(a+b)(a-b)=a^2-b^2$$: $$(1+\sqrt{5})(1-\sqrt{5})=1-5=-4$$.

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Joined: 20 Dec 2013
Posts: 225
Location: India

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02 Jan 2014, 06:54
1
Quite a simple question:(a+b)*(a-b)=a^2-b^2
So,(1+5^1/2)(1-5^1/2)=1-5=-4
Option A should be the answer.
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Joined: 25 Apr 2012
Posts: 669
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03 Jan 2014, 00:41
(1+\sqrt{5})(1-\sqrt{5})=

(A) -4
(B) 2
(C) 6
(D) -4-2\sqrt{5}
(E) 6-2\sqrt{5}

Sol: We know a^2-b^2= (a-b)(a+b).

Therefore the above can be re-written as (1^2-\sqrt{5}^2)------>(1-5)= -4 Ans A
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Math Expert
Joined: 02 Sep 2009
Posts: 55618

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05 Jan 2014, 11:18
SOLUTION

$$(1+\sqrt{5})(1-\sqrt{5})=$$

(A) -4
(B) 2
(C) 6
(D) $$-4-2\sqrt{5}$$
(E) $$6-2\sqrt{5}$$

Apply $$(a+b)(a-b)=a^2-b^2$$: $$(1+\sqrt{5})(1-\sqrt{5})=1-5=-4$$.

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Joined: 22 Sep 2015
Posts: 91
(1 + √5)(1 - √5)  [#permalink]

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24 Aug 2016, 09:13
$$(1 + \sqrt{5})(1 - \sqrt{5})$$ =

a) $$-4$$
b) $$-2$$
c) $$6$$
d) $$-4 - 2\sqrt{5}$$
e) $$6 - 2\sqrt{5}$$
Math Expert
Joined: 02 Sep 2009
Posts: 55618

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24 Aug 2016, 09:38
nycgirl212 wrote:
$$(1 + \sqrt{5})(1 - \sqrt{5})$$ =

a) $$-4$$
b) $$-2$$
c) $$6$$
d) $$-4 - 2\sqrt{5}$$
e) $$6 - 2\sqrt{5}$$

Merging topics. Please refer to the discussion above.
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Joined: 09 Sep 2013
Posts: 11368

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15 Sep 2018, 23:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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: (1+5^1/2)(1-5^1/2)=   [#permalink] 15 Sep 2018, 23:54
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